WorldWideScience

Sample records for monterey-miami parabolic equation

  1. An Examination of Higher-Order Treatments of Boundary Conditions in Split-Step Fourier Parabolic Equation Models

    Science.gov (United States)

    2015-06-01

    HIGHER-ORDER TREATMENTS OF BOUNDARY CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS by Savas Erdim June 2015 Thesis Advisor...CONDITIONS IN SPLIT-STEP FOURIER PARABOLIC EQUATION MODELS 5. FUNDING NUMBERS 6. AUTHOR(S) Savas Erdim 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES... Parabolic equation models solved using the split-step Fourier (SSF) algorithm, such as the Monterey Miami Parabolic Equation model, are commonly used

  2. Invariant foliations for parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    It is proved for parabolic equations that under certain conditions the weak (un-)stable manifolds possess invariant foliations, called strongly (un-)stable foliations. The relevant results on center manifolds are generalized to weak hyperbolic manifolds.

  3. Numerical Solution of Parabolic Equations

    DEFF Research Database (Denmark)

    Østerby, Ole

    These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory....... Among the special features of this book can be mentioned the presentation of a practical approach to reliable estimates of the global error, including warning signals if the reliability is questionable. The technique is generally applicable for estimating the discretization error in numerical...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...

  4. International Workshop on Elliptic and Parabolic Equations

    CERN Document Server

    Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

    2015-01-01

    This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

  5. Partial differential equations of parabolic type

    CERN Document Server

    Friedman, Avner

    2008-01-01

    This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman - Director of the Mathematical Biosciences Institute at The Ohio State University - offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning fundamenta

  6. Homogenization of a nonlinear degenerate parabolic equation

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    The homogenization of one kind of nonlinear parabolic equation is studied. The weak convergence and corrector results are obtained by combining carefully the compactness method and two-scale convergence method in the homogenization theory.

  7. POSITIVE EQUILIBRIUM SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions:"subsolution (≤) supersolution", the existence and stability/instability of equilibrium solutions are obtained.

  8. Orbit Connections in a Parabolic Equation.

    Science.gov (United States)

    1983-04-01

    Departamento de Matematica , 13560, Slo Carlos, S.P. Brasil. This research has been supported in part by CAPES-qoordena~io de Aperfeiqoamento de Pessoal...de Nivel Superior , Brasilia, D.F., Brasil under contract Proc. #3056/78. 1k ORBIT CONNECTIONS IN A PARABOLIC EQUATION by Jack K. Hale and Arnaldo S

  9. An Approximation of Ultra-Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2012-01-01

    Full Text Available The first and second order of accuracy difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations are presented. Stability of these difference schemes is established. Theoretical results are supported by the result of numerical examples.

  10. ANISOTROPIC PARABOLIC EQUATIONS WITH MEASURE DATA

    Institute of Scientific and Technical Information of China (English)

    Li Fengquan; Zhao Huixiu

    2001-01-01

    In this paper, we prove the existence of solutions to anisotropic parabolic equations with right hand side term in the bounded Radon measure M(Q) and the initial condition in M(Ω) or in Lm space (with m "small").

  11. Moving interfaces and quasilinear parabolic evolution equations

    CERN Document Server

    Prüss, Jan

    2016-01-01

    In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...

  12. The quasilinear parabolic kirchhoff equation

    Directory of Open Access Journals (Sweden)

    Dawidowski Łukasz

    2017-04-01

    Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.

  13. Antiperiodic Problems for Nonautonomous Parabolic Evolution Equations

    Directory of Open Access Journals (Sweden)

    R. N. Wang

    2014-01-01

    Full Text Available This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form u′(t=A(tu(t+f(t,u(t, t∈R, u(t+T=-u(t, t∈R, where (Att∈R (possibly unbounded, depending on time, is a family of closed and densely defined linear operators on a Banach space X. Upon making some suitable assumptions such as the Acquistapace and Terreni conditions and exponential dichotomy on (Att∈R, we obtain the existence results of antiperiodic mild solutions to such problem. The antiperiodic problem of nonautonomous semilinear parabolic evolution equation of neutral type is also considered. As sample of application, these results are applied to, at the end of the paper, an antiperiodic problem for partial differential equation, whose operators in the linear part generate an evolution family of exponential stability.

  14. SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    G. Dziuk; C.M. Elliott

    2007-01-01

    In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.

  15. Concentration phenomena in the semilinear parabolic equation

    Institute of Scientific and Technical Information of China (English)

    TAN; Zhong

    2001-01-01

    [1]Fujita, H., On the blowing up of solutions of the Chauch problem for u=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I, 966, 3: 09.[2]Ni, W. -M., Sacks, P. E., Tavantzis, J., On the asymptotic behavior of solutions of certain quasilinear equations of parabolic type, J. Differential Equations, 984, 54: 97.[3]Cazenave, T., Lions, P. L., Solutions globales d'equations de la chaleur semilineaires, Comm. in Partial Differential Equations, 984, 9(0): 955.[4]Giga, Y., A bound for global solutions of semilinear heat equations, Commun. Math. Phys., 986, 03: 45.[5]Galaktionov, V., Vazquez, J. L., Continuation of blow-up solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math., 997, 50: .[6]Rey, O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Func. Anal., 990, 89: .[7]Wei Juncheng, Asymptotic behavior of least energy solution to a semilinear Dirichlet problem near the critical exponent, J. Math. Soc. Japan, 998, 50(): 39.[8]Lions, P. L., The concentration-compactness principle in the calculus of variations, The limit case ,2, Rev. Mat. Iberoamerioana, 985, : 45, 45.[9]Brezis, H., Elliptic equations with limiting Sobolev exponents——the impact of topology, Commun. Pure and Appl. Math., 986, XXXXIX: S7.[10]Sacks, J., Uhlenbeck, K., The existence of minimal immersions of 2-spheres, Ann. Math., 98, 3: .[11]Zhu Xiping, Nontrivial solutions of quasilinear elliptic equation involving critical growth, Science in China (in Chinese), Ser. A, 988, (3): 225.[12]Pohozaev, S. I., Eigenfunctions of the equation -Δu+λf(u)=0, Soviet. Math. Dold., 965, 6: 408.[13]Gidas, B., Ni, W. -M., Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 979, 68: 209.[14]Ni, W. -M., Sacks, P. E., Singular behaviour in nonlinear parabolic equations, Tran. of the AMS, 985, 287(2): 657.[15]Ni, W. -M., Sacks, P. E

  16. Optimal Wentzell Boundary Control of Parabolic Equations

    Energy Technology Data Exchange (ETDEWEB)

    Luo, Yousong, E-mail: yousong.luo@rmit.edu.au [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

    2017-04-15

    This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

  17. New method to solve electromagnetic parabolic equation

    Institute of Scientific and Technical Information of China (English)

    赵小峰; 黄思训; 康林春

    2013-01-01

    This paper puts forward a new method to solve the electromagnetic parabolic equation (EMPE) by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo-lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana-lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.

  18. A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    YU Xijun

    2005-01-01

    A combination of the classical Newton Method and the multigrid method, i.e.,a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O(NNk) similar to multigrid method for linear parabolic problems.

  19. Bifurcation and stability for a nonlinear parabolic partial differential equation

    Science.gov (United States)

    Chafee, N.

    1973-01-01

    Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.

  20. Almost Periodic Viscosity Solutions of Nonlinear Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Zhang Shilin

    2009-01-01

    Full Text Available We generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations under usual hypotheses.

  1. Upper bounds for parabolic equations and the Landau equation

    Science.gov (United States)

    Silvestre, Luis

    2017-02-01

    We consider a parabolic equation in nondivergence form, defined in the full space [ 0 , ∞) ×Rd, with a power nonlinearity as the right-hand side. We obtain an upper bound for the solution in terms of a weighted control in Lp. This upper bound is applied to the homogeneous Landau equation with moderately soft potentials. We obtain an estimate in L∞ (Rd) for the solution of the Landau equation, for positive time, which depends only on the mass, energy and entropy of the initial data.

  2. Carleman Estimates for Parabolic Equations with Nonhomogeneous Boundary Conditions

    Institute of Scientific and Technical Information of China (English)

    Oleg Yu IMANUVILOV; Jean Pierre PUEL; Masahiro YAMAMOTO

    2009-01-01

    The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions.On the basis of this estimate,improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained.This system can be viewed as an approximation of the Stokes system.

  3. The parabolic equation method for outdoor sound propagation

    DEFF Research Database (Denmark)

    Arranz, Marta Galindo

    The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations...

  4. OSCILLATION OF NONLINEAR IMPULSIVE PARABOLIC DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS

    Institute of Scientific and Technical Information of China (English)

    CuiChenpei; ZouMin; LiuAnping; XiaoLi

    2005-01-01

    In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equations with several delays are investigated and a series of new sufficient conditions for oscillations of the equation are established.

  5. Homogenization of attractors for a class of nonlinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    WANG Guo-lian; ZHANG Xing-you

    2004-01-01

    The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.

  6. The homogenization of a class of degenerate quasilinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xingyou; HUANG Yong

    2003-01-01

    The homogenization of a class of degenerate quasilinear parabolic equations is studied. The Ap weight theory and the classical compensated compactness method are incorporated to obtain the homogenized equation.

  7. On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order

    Institute of Scientific and Technical Information of China (English)

    Zhen Hai LIU

    2005-01-01

    We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order, which can degenerate, on a part of the boundary, on a segment in the interior of the domain and in time.

  8. IDENTIFICATION OF PARAMETERS IN PARABOLIC EQUATIONS WITH NONLINEARITY

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, we consider the identification of parameters in parabolic equations with nonlinearity. Some approximation processes for the identification problem are given. Our results improve and generalize the previous results.

  9. Differentiability at lateral boundary for fully nonlinear parabolic equations

    Science.gov (United States)

    Ma, Feiyao; Moreira, Diego R.; Wang, Lihe

    2017-09-01

    For fully nonlinear uniformly parabolic equations, the first derivatives regularity of viscosity solutions at lateral boundary is studied under new Dini type conditions for the boundary, which is called Reifenberg Dini conditions and is weaker than usual Dini conditions.

  10. Quasiconformal mappings and degenerate elliptic and parabolic equations

    Directory of Open Access Journals (Sweden)

    Filippo Chiarenza

    1987-11-01

    Full Text Available In this paper two Harnak inequalities are proved concerning a degenerate elliptic and a degenerate parabolic equation. In both cases the weight giving the degeneracy is a power of the jacobian of a quasiconformal mapping.

  11. Comparison principle for parabolic equations in the Heisenberg group

    Directory of Open Access Journals (Sweden)

    Thomas Bieske

    2005-09-01

    Full Text Available We define two notions of viscosity solutions to parabolic equations in the Heisenberg group, depending on whether the test functions concern only the past or both the past and the future. We then exploit the Heisenberg geometry to prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.

  12. On some perturbation techniques for quasi-linear parabolic equations

    Directory of Open Access Journals (Sweden)

    Igor Malyshev

    1990-01-01

    Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

  13. The fundamental solutions for fractional evolution equations of parabolic type

    Directory of Open Access Journals (Sweden)

    Mahmoud M. El-Borai

    2004-01-01

    Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

  14. Chernoff's distribution and parabolic partial differential equations

    NARCIS (Netherlands)

    P. Groeneboom; S.P. Lalley; N.M. Temme (Nico)

    2013-01-01

    textabstractWe give an alternative route to the derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift, using the Feynman-Kac formula with stopping times. The derivation also uses an interesting

  15. Chernoff's distribution and parabolic partial differential equations

    NARCIS (Netherlands)

    P. Groeneboom; S.P. Lalley; N.M. Temme (Nico)

    2013-01-01

    textabstractWe give an alternative route to the derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift, using the Feynman-Kac formula with stopping times. The derivation also uses an interesting relatio

  16. MAXIMUM PRINCIPLES FOR SECOND-ORDER PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Antonio Vitolo

    2004-01-01

    This paper is the parabolic counterpart of previous ones about elliptic operators in unbounded domains. Maximum principles for second-order linear parabolic equations are established showing a variant of the ABP-Krylov-Tso estimate, based lower bound for super-solutions due to Krylov and Safonov. The results imply the uniqueness for the Cauchy-Dirichlet problem in a large class of infinite cylindrical and non-cylindrical domains.

  17. A Microscopic Convexity Principle for Spacetime Convex Solutions of Fully Nonlinear Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    Chuan Qiang CHEN; Bo Wen HU

    2013-01-01

    We study microscopic spacetime convexity properties of fully nonlinear parabolic partial differential equations.Under certain general structure condition,we establish a constant rank theorem for the spacetime convex solutions of fully nonlinear parabolic equations.At last,we consider the parabolic convexity of solutions to parabolic equations and the convexity of the spacetime second fundamental form of geometric flows.

  18. NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    崔霞

    2002-01-01

    A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD,the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1- and L2-norm space estimates and the O((△t)2) estimate for time variable are obtained.

  19. Decomposition method for solving parabolic equations in finite domains

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    This paper presents a comparison among Adomian decomposition method (ADM), Wavelet-Galerkin method (WGM),the fully explicit (1,7) finite difference technique (FTCS), the fully implicit (7,1) finite difference method (BTCS), (7,7)Crank-Nicholson type finite difference formula (C-N), the fully explicit method (1,13) and 9-point finite difference method, for solving parabolic differential equations with arbitrary boundary conditions and based on weak form functionals in finite domains.The problem is solved rapidly, easily and elegantly by ADM. The numerical results on a 2D transient heat conducting problem and 3D diffusion problem are used to validate the proposed ADM as an effective numerical method for solving finite domain parabolic equations. The numerical results showed that our present method is less time consuming and is easier to use than other methods. In addition, we prove the convergence of this method when it is applied to the nonlinear parabolic equation.

  20. Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators

    CERN Document Server

    Caffarelli, Luis; Nirenberg, Louis

    2011-01-01

    The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma for viscosity solutions including also parabolic equations.

  1. Regularity for solutions of non local parabolic equations

    CERN Document Server

    Lara, Héctor A Chang

    2011-01-01

    We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We proof $C^\\a$ regularity in space and time and for translation invariant equations and under different assumptions on the kernels $C^{1,\\a}$ in space and time regularity. The proofs rely on a weak parabolic ABP inspired in recent work done by L. Silvestre and the classic ideas of K. Tso and L. Wang. Our results remain uniform as $\\s\\to2$ allowing us to understand the non local theory as an extension to the classical one.

  2. Nonlinear Parabolic Equations with Singularities in Colombeau Vector Spaces

    Institute of Scientific and Technical Information of China (English)

    Mirjana STOJANOVI(C)

    2006-01-01

    We consider nonlinear parabolic equations with nonlinear non-Lipschitz's term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space gC1,w2,2([O,T),Rn),n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space gC1,L2([O,T),Rn),n ≤ 3.

  3. Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Michael Gil'

    2016-01-01

    Full Text Available We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.

  4. Propagation equation for tight-focusing by a parabolic mirror.

    Science.gov (United States)

    Couairon, A; Kosareva, O G; Panov, N A; Shipilo, D E; Andreeva, V A; Jukna, V; Nesa, F

    2015-11-30

    Part of the chain in petawatt laser systems may involve extreme focusing conditions for which nonparaxial and vectorial effects have high impact on the propagation of radiation. We investigate the possibility of using propagation equations to simulate numerically the focal spot under these conditions. We derive a unidirectional propagation equation for the Hertz vector, describing linear and nonlinear propagation under situations where nonparaxial diffraction and vectorial effects become significant. By comparing our simulations to the results of vector diffraction integrals in the case of linear tight-focusing by a parabolic mirror, we establish a practical criterion for the critical f -number below which initializing a propagation equation with a parabolic input phase becomes inaccurate. We propose a method to find suitable input conditions for propagation equations beyond this limit. Extreme focusing conditions are shown to be modeled accurately by means of numerical simulations of the unidirectional Hertz-vector propagation equation initialized with suitable input conditions.

  5. Almost periodic solutions to systems of parabolic equations

    Directory of Open Access Journals (Sweden)

    Janpou Nee

    1994-01-01

    Full Text Available In this paper we show that the second-order differential solution is 2-almost periodic, provided it is 2-bounded, and the growth of the components of a non-linear function of a system of parabolic equation is bounded by any pair of con-secutive eigenvalues of the associated Dirichlet boundary value problems.

  6. Improved Green's function parabolic equation method for atmospheric sound propagation

    NARCIS (Netherlands)

    Salomons, E.M.

    1998-01-01

    The numerical implementation of the Green's function parabolic equation (GFPE) method for atmospheric sound propagation is discussed. Four types of numerical errors are distinguished: (i) errors in the forward Fourier transform; (ii) errors in the inverse Fourier transform; (iii) errors in the refra

  7. Stability test for a parabolic partial differential equation

    NARCIS (Netherlands)

    Vajta, Miklos

    2001-01-01

    The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer.

  8. Nyquist stability test for a parabolic partial differential equation

    NARCIS (Netherlands)

    Vajta, Miklos; Hamza, M.H.

    2000-01-01

    The paper describes a Nyquist stability test applied to a parabolic partial differential equation. The PDE describes the temperature distribution of composite structures with linear inner heat source. The distributed transfer functions have been developed by the transmission matrix method. To

  9. Parabolic vortex equations and instantons of infinite energy

    Science.gov (United States)

    Biquard, Olivier; García-Prada, Oscar

    1997-02-01

    We study the vortex equations on parabolic bundles over a Riemann surface and prove a Hitchin-Kobayashi-type correspondence relating the existence of solutions to a certain stability condition. This is achieved by translating our problem into a four-dimensional one, via dimensional reduction arguments. In return we obtain examples of instantons of infinite energy.

  10. On an algorithm for solving parabolic and elliptic equations

    Science.gov (United States)

    D'Ascenzo, N.; Saveliev, V. I.; Chetverushkin, B. N.

    2015-08-01

    The present-day rapid growth of computer power, in particular, parallel computing systems of ultrahigh performance requires a new approach to the creation of models and solution algorithms for major problems. An algorithm for solving parabolic and elliptic equations is proposed. The capabilities of the method are demonstrated by solving astrophysical problems on high-performance computer systems with massive parallelism.

  11. Null controllability for a fourth order parabolic equation

    Institute of Scientific and Technical Information of China (English)

    YU Hang

    2009-01-01

    In the paper,the null interior controllability for a fourth order parabolic equation is obtained.The method Is based on Lebeau-Rabbiano inequality which is a quantitative unique continuation property for the sum of eigenfunctions of the Laplacian.

  12. Anisotropic uniqueness classes for a degenerate parabolic equation

    Energy Technology Data Exchange (ETDEWEB)

    Vil' danova, V F [Bashkir State Pedagogical University, Ufa (Russian Federation); Mukminov, F Kh [Bashkir State University, Ufa (Russian Federation)

    2013-11-30

    Anisotropic uniqueness classes of Tacklind type are identified for a degenerate linear parabolic equation of the second order in an unbounded domain. The Cauchy problem and mixed problems with boundary conditions of the first and third type are considered. Bibliography: 18 titles.

  13. Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations

    Institute of Scientific and Technical Information of China (English)

    Yun Hua OU; Alemdar HASANOV; Zhen Hai LIU

    2008-01-01

    This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.

  14. APPROXIMATE CONTROLLABILITY OF A CLASS OF QUASILINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Wang Chunpeng; Yin Jingxue; Huang Xingbo

    2002-01-01

    In this paper we study the approximate controllability of a class ofquasilinear parabolic equations in a bounded spacial domain Ω RN when the controlacts on any open and nonempty subset of Ω. The approximate controllability inLp(Ω)for N + 2 ≤ p < +∞ is proved. The proof combines a variational approach to thecontrollability problem for linear equations and a fixed point method.

  15. Concentration phenomena in the semilinear parabolic equation

    Institute of Scientific and Technical Information of China (English)

    谭忠

    2001-01-01

    We prove the existence of the global, but unbounded solution of the semilinear heat equations with critical Sobolev exponent, and that under some assumptions, the global unbounded classical solution concentrates on origin as t→∞.

  16. Darboux transformations and linear parabolic partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Arrigo, Daniel J.; Hickling, Fred [Department of Mathematics, University of Central Arkansas, Conway, AR (United States)

    2002-07-19

    Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor.

  17. Local H\\"older continuity for doubly nonlinear parabolic equations

    CERN Document Server

    Kuusi, Tuomo; Urbano, José Miguel

    2010-01-01

    We give a proof of the H\\"older continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling non-trivial Borel measure which supports a Poincar\\'e inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.

  18. Long term behaviour of singularly perturbed parabolic degenerated equation

    Directory of Open Access Journals (Sweden)

    Ibrahima Faye

    2016-12-01

    Full Text Available In this paper we consider models built in [4] for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a periodic-in-time-and-space solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.

  19. Tropospheric Refraction Modeling Using Ray-Tracing and Parabolic Equation

    Directory of Open Access Journals (Sweden)

    P. Pechac

    2005-12-01

    Full Text Available Refraction phenomena that occur in the lower atmospheresignificantly influence the performance of wireless communicationsystems. This paper provides an overview of corresponding computationalmethods. Basic properties of the lower atmosphere are mentioned.Practical guidelines for radiowave propagation modeling in the loweratmosphere using ray-tracing and parabolic equation methods are given.In addition, a calculation of angle-of-arrival spectra is introducedfor multipath propagation simulations.

  20. A stability analysis for a semilinear parabolic partial differential equation

    Science.gov (United States)

    Chafee, N.

    1973-01-01

    The parabolic partial differential equation considered is u sub t = u sub xx + f(u), where minus infinity x plus infinity and o t plus infinity. Under suitable hypotheses pertaining to f, a class of initial data is exhibited: phi(x), minus infinity x plus infinity, for which the corresponding solutions u(x,t) appraoch zero as t approaches the limit of plus infinity. This convergence is uniform with respect to x on any compact subinterval of the real axis.

  1. Long term behaviour of singularly perturbed parabolic degenerated equation

    CERN Document Server

    Faye, Ibrahima; Seck, Diaraf

    2011-01-01

    In this paper we consider models for short-term, mean-term and long-term morphodynamics of dunes and megariples. We give an existence and uniqueness result for long term dynamics of dunes. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the mean-term and long-term models are homogenized.

  2. Singular solutions of doubly singular parabolic equations with absorption

    Directory of Open Access Journals (Sweden)

    Yuanwei Qi

    2000-11-01

    Full Text Available In this paper we study a doubly singular parabolic equation with absorption, $$ u_t = hbox{ m div} ( |abla u^m|^{p-2}abla u^m -u^q $$ with $m>0$, $p>1$, $m(p-11$. We give a complete classification of solutions, which we call singular, that are non-negative, non-trivial, continuous in ${mathbb R}^n imes [0, inftybackslash{(0,0} $, and satisfy $u(x,0=0$ for all $xeq 0$. Applications of similar but simpler equations show that these solutions are very important in the study of intermediate asymptotic behavior of general solutions.

  3. HOMOGENIZATION OF SEMILINEAR PARABOLIC EQUATIONS IN PERFORATED DOMAINS

    Institute of Scientific and Technical Information of China (English)

    P.DONATO; A. NABIL

    2004-01-01

    This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated by e-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as e → 0 is described, and the limit equation is given.

  4. Wavelet Method for Numerical Solution of Parabolic Equations

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    A. H. Choudhury

    2014-01-01

    Full Text Available We derive a highly accurate numerical method for the solution of parabolic partial differential equations in one space dimension using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method using some special types of basis functions obtained by integrating Daubechies functions which are compactly supported and differentiable. The time variable is discretized by using various classical finite difference schemes. Theoretical and numerical results are obtained for problems of diffusion, diffusion-reaction, convection-diffusion, and convection-diffusion-reaction with Dirichlet, mixed, and Neumann boundary conditions. The computed solutions are highly favourable as compared to the exact solutions.

  5. ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION

    KAUST Repository

    MARKOWICH, P. A.

    2009-10-01

    We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.

  6. Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition

    Directory of Open Access Journals (Sweden)

    Deniz Agirseven

    2012-01-01

    Full Text Available Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. A procedure of modified Gauss elimination method is used for the solution of these difference schemes. Homotopy analysis method is applied. Comparison of finite difference and homotopy analysis methods is given on the problem.

  7. ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Guang-wei Yuan; Xu-deng Hang

    2006-01-01

    This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.

  8. A cell complex structure for the space of heteroclines for a semilinear parabolic equation

    Directory of Open Access Journals (Sweden)

    Michael Robinson

    2009-01-01

    Full Text Available It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite dimensional unstable manifolds. In this article, these results are unified to show that for a specific parabolic equation on an unbounded domain, the space of heteroclinic orbits has a cell complex structure with finite dimensional cells. The result depends crucially on the choice of spatial dimension and the degree of the nonlinearity in the parabolic equation, and thereby requires some delicate treatment.

  9. A comparison principle for singular parabolic equations in the Heisenberg group

    Directory of Open Access Journals (Sweden)

    Pablo Ochoa

    2015-04-01

    Full Text Available In this work, we prove a comparison principle for singular parabolic equations with boundary conditions in the context of the Heisenberg group. In particular, this result applies to interesting equations, such as the parabolic infinite Laplacian, the mean curvature flow equation and more general homogeneous diffusions.

  10. Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

    Science.gov (United States)

    Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

    2011-06-01

    The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.

  11. Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

    Directory of Open Access Journals (Sweden)

    K. Atifi

    2017-01-01

    Full Text Available A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient. Some numerical experiments are given.

  12. Optimal Control of a Parabolic Equation with Dynamic Boundary Condition

    Energy Technology Data Exchange (ETDEWEB)

    Hoemberg, D., E-mail: hoemberg@wias-berlin.de; Krumbiegel, K., E-mail: krumbieg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems (Germany); Rehberg, J., E-mail: rehberg@wias-berlin.de [Weierstrass Institute for Applied Mathematics and Stochastics, Partial Differential Equations (Germany)

    2013-02-15

    We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.

  13. INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.

  14. Strong solutions of semilinear parabolic equations with measure data and generalized backward stochastic differential equations

    CERN Document Server

    Klimsiak, Tomasz

    2010-01-01

    We prove that under natural assumptions on the data strong solutions in Sobolev spaces of semilinear parabolic equations in divergence form involving measure on the right-hand side may be represented by solutions of some generalized backward stochastic differential equations. As an application we provide stochastic representation of strong solutions of the obstacle problem be means of solutions of some reflected backward stochastic differential equations. To prove the latter result we use a stochastic homographic approximation for solutions of the reflected backward equation. The approximation may be viewed as a stochastic analogue of the homographic approximation for solutions to the obstacle problem.

  15. Global attractors of a degenerate parabolic equation and their error estimates

    Institute of Scientific and Technical Information of China (English)

    HU Xiaohong; ZHANG Xingyou

    2004-01-01

    The existences of the global attractor A? for a degenerate parabolic equation and of the homogenized attractorA0 for the corresponding homogenized equation are studied, and explicit estimates for the distance between A? and A0 are given.

  16. Instability of positive periodic solutions for semilinear pseudo-parabolic equations with logarithmic nonlinearity

    Science.gov (United States)

    Ji, Shanming; Yin, Jingxue; Cao, Yang

    2016-11-01

    In this paper, we consider the periodic problem for semilinear heat equation and pseudo-parabolic equation with logarithmic source. After establishing the existence of positive periodic solutions, we discuss the instability of such solutions.

  17. Nonlocal operators, parabolic-type equations, and ultrametric random walks

    Energy Technology Data Exchange (ETDEWEB)

    Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx [Centro de Investigacion y de Estudios Avanzados del I.P.N., Departamento de Matematicas, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico D.F., C.P. 07360 (Mexico)

    2013-11-15

    In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.

  18. A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology

    Science.gov (United States)

    Del Bene, Kevin; Lingevitch, Joseph; Doschek, George

    2016-08-01

    A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.

  19. Cntinuity of Some Classes of Functions Related to Degenerate Parabolic Equations and Its Applications

    Institute of Scientific and Technical Information of China (English)

    宋斌恒; 袁聪

    2002-01-01

    We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equationsl.Comsequently,we prove that a function in such a class is continuous.As an application,we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form,including the anisotropic porous equations.

  20. Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions

    Institute of Scientific and Technical Information of China (English)

    A.M. Il'in; R.Z. Khasminskii; G. Yin

    2002-01-01

    This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.

  1. A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we investigate the Legendre Galerkin spectral approximation of quadratic optimal control problems governed by parabolic equations.A spectral approximation scheme for the parabolic optimal control problem is presented.We obtain a posteriori error estimates of the approximated solutions for both the state and the control.

  2. Null exact controllability of the parabolic equations with equivalued surface boundary condition

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available This paper is devoted to showing the null exact controllability for a class of parabolic equations with equivalued surface boundary condition. Our method is based on the duality argument and global Carleman-type estimate for a parabolic operator.

  3. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Jiebao Sun

    2011-01-01

    parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  4. H(o)lder Continuity of Weak Solutions for Parabolic Equations with Nonstandard Growth Conditions

    Institute of Scientific and Technical Information of China (English)

    Meng XU; Ya Zhe CHEN

    2006-01-01

    In this paper, we investigate the interior regularity including the local boundedness and the interior H(o)lder continuity of weak solutions for parabolic equations of the p(x,t)-Laplacian type. We improve the Moser iteration technique and generalize the known results for the elliptic problem to the corresponding parabolic problem.

  5. Linearization models for parabolic dynamical systems via Abel's functional equation

    CERN Document Server

    Elin, Mark; Reich, Simeon; Shoikhet, David

    2009-01-01

    We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups. The crucial point is that these solutions are univalent functions convex in one direction. In a parallel direction, we find analytic conditions which determine certain geometric properties of those functions, such as the location of their images in either a half-plane or a strip, and their containing either a half-plane or a strip. In the context of semigroup theory these geometric questions may be interpreted as follows: is a given one-parameter continuous semigroup either an outer or an inner conjugate of a group of automorphisms? In other words, the problem is finding a fractional linear model of the semigroup which is defined by a group of automorphisms of the open unit disk. Our results enable us to establish some new important analytic and geometric characteristics of t...

  6. Three-dimensional parabolic equation modeling of mesoscale eddy deflection.

    Science.gov (United States)

    Heaney, Kevin D; Campbell, Richard L

    2016-02-01

    The impact of mesoscale oceanography, including ocean fronts and eddies, on global scale low-frequency acoustics is examined using a fully three-dimensional parabolic equation model. The narrowband acoustic signal, for frequencies from 2 to 16 Hz, is simulated from a seismic event on the Kerguellen Plateau in the South Indian Ocean to an array of receivers south of Ascension Island in the South Atlantic, a distance of 9100 km. The path was chosen for its relevance to seismic detections from the HA10 Ascension Island station of the International Monitoring System, for its lack of bathymetric interaction, and for the dynamic oceanography encountered as the sound passes the Cape of Good Hope. The acoustic field was propagated through two years (1992 and 1993) of the eddy-permitting ocean state estimation ECCO2 (Estimating the Circulation and Climate of the Ocean, Phase II) system. The range of deflection of the back-azimuth was 1.8° with a root-mean-square of 0.34°. The refraction due to mesoscale oceanography could therefore have significant impacts upon localization of distant low-frequency sources, such as seismic or nuclear test events.

  7. Parabolic Equations in Musielak-Orlicz-Sobolev Spaces

    Directory of Open Access Journals (Sweden)

    M.L. Ahmed Oubeid

    2013-11-01

    Full Text Available We prove in this paper the existence of solutions of nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces. An approximation and a trace results in inhomogeneous Musielak-Orlicz-Sobolev spaces have also been provided.

  8. Time-periodic Solution to a Nonlinear Parabolic Type Equation of Higher Order

    Institute of Scientific and Technical Information of China (English)

    Yan-ping Wang; You-lin Zhang

    2008-01-01

    In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Gaierkin method.

  9. EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR A NONLINEAR PARABOLIC EQUATION RELATED TO IMAGE ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    Wang Lihe; Zhou Shulin

    2006-01-01

    In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in image analysis.

  10. Time-Periodic Solution of a 2D Fourth-Order Nonlinear Parabolic Equation

    Indian Academy of Sciences (India)

    Xiaopeng Zhao; Changchun Liu

    2014-08-01

    By using the Galerkin method, we study the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a fourth-order nonlinear parabolic equation in 2D case.

  11. The Rothe's Method to a Parabolic Integrodifferential Equation with a Nonclassical Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Abdelfatah Bouziani

    2010-01-01

    the weak solvability of parabolic integrodifferential equations with a nonclassical boundary conditions. The investigation is made by means of approximation by the Rothes method which is based on a semidiscretization of the given problem with respect to the time variable.

  12. LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LI Fengquan

    2002-01-01

    In this paper, we discuss the limit behaviour of solutions to equivalued surface boundary value problem for parabolic equations when the equivalued surface boundary shrinks to a point and the space dimension of the domain is two or more.

  13. Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition

    Institute of Scientific and Technical Information of China (English)

    王明新

    2001-01-01

    This paper deals with the blow-up rate estimates of solutions for semilinear parabolic systems coupled in an equation and a boundary condition. The upper and lower bounds of blow-up rates have been obtained.

  14. TRAVELING WAVE FRONTS OF A DEGENERATE PARABOLIC EQUATION WITH NON-DIVERGENCE FORM

    Institute of Scientific and Technical Information of China (English)

    王春朋; 尹景学

    2003-01-01

    We study the traveling wave solutions of a nonlinear degenerate parabolic equation with non-divergence form. Under some conditions on the source, we establish the existence, and then discuss the regularity of such solutions.

  15. AN UPPER ESTIMATE OF SOLUTION FOR A GENERALCLASS OF PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Li Shenghong; Wang Xuefeng

    2000-01-01

    The upper estimates of the functions that satisfy some differentialintegral inequality are established in this paper. We obtain the uniform estimates of maximum of the solutions for a general class of parabolic equations and extend some known results.

  16. Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

    Institute of Scientific and Technical Information of China (English)

    Xi Cheng ZHANG

    2004-01-01

    In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions, by the way, we obtain the quasi-sure continuity of the solution.

  17. Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Weifeng Wang

    2014-01-01

    Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

  18. Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions

    Directory of Open Access Journals (Sweden)

    Diabate Nabongo

    2008-01-01

    Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.

  19. Sound field computations in the Bay of Bengal using parabolic equation method

    Digital Repository Service at National Institute of Oceanography (India)

    Navelkar, G.S.; Somayajulu, Y.K.; Murty, C.S.

    Effect of the cold core eddy in the Bay of Bengal on acoustic propagation was analysed by parabolic equation (PE) method. Source depth, frequency and propagation range considered respectively for the two numerical experiments are 150 m, 400 Hz, 650...

  20. Homogenization of a Parabolic Equation in Perforated Domain with Neumann Boundary Condition

    Indian Academy of Sciences (India)

    A K Nandakumaran; M Rajesh

    2002-02-01

    In this article, we study the homogenization of the family of parabolic equations over periodically perforated domains \\begin{align*}_tb\\left(\\frac{x}{}, u_{}\\right)-\\mathrm{div} a\\left(\\frac{x}{}, u_{},\

  1. THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION WITH Lp INITIAL VALUE

    Institute of Scientific and Technical Information of China (English)

    Wang Zhigang; Li Yachun

    2012-01-01

    The aim of this paper is to prove the well-posedness (existence and uniqueness)of the Lp entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.

  2. Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient

    Science.gov (United States)

    Ashyralyev, Allaberen; Okur, Ulker

    2016-08-01

    In the present paper, the Crank-Nicolson difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, convergence estimates for the solution of difference schemes for the numerical solution of three mixed problems for parabolic equations are obtained. The numerical results are given.

  3. Integration of equations of parabolic type by the method of nets

    CERN Document Server

    Saul'Yev, V K; Stark, M; Ulam, S

    1964-01-01

    International Series of Monographs in Pure and Applied Mathematics, Volume 54: Integration of Equations of Parabolic Type by the Method of Nets deals with solving parabolic partial differential equations using the method of nets. The first part of this volume focuses on the construction of net equations, with emphasis on the stability and accuracy of the approximating net equations. The method of nets or method of finite differences (used to define the corresponding numerical method in ordinary differential equations) is one of many different approximate methods of integration of partial diff

  4. Schauder estimates for parabolic equation of bi-harmonic type

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got.out approach is simple and straightforward.

  5. The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic Degeneracy

    Institute of Scientific and Technical Information of China (English)

    Guo Chun WEN

    2006-01-01

    This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness and existence of solutions are proved by a new method.

  6. Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation

    Institute of Scientific and Technical Information of China (English)

    Guo Jin-yong

    2013-01-01

    We consider an initial-boundary value problem for a p-biharmonic parabo-lic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.

  7. A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

    Directory of Open Access Journals (Sweden)

    Yang Liu

    2012-01-01

    Full Text Available A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

  8. Some blow-up problems for a semilinear parabolic equation with a potential

    Science.gov (United States)

    Cheng, Ting; Zheng, Gao-Feng

    The blow-up rate estimate for the solution to a semilinear parabolic equation u=Δu+V(x)|u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].

  9. A gradient estimate for solutions to parabolic equations with discontinuous coefficients

    Directory of Open Access Journals (Sweden)

    Jishan Fan

    2013-04-01

    Full Text Available Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codimension 1, which we called them emph{manifolds of discontinuities}. Their gradient estimate is independent of the distances between manifolds of discontinuities. In this paper, we gave a parabolic version of their results. That is, we gave a gradient estimate for parabolic equations of divergence forms with piecewise smooth coefficients. The coefficients are assumed to be independent of time and their discontinuities are likewise the previous elliptic equations. As an application of this estimate, we also gave a pointwise gradient estimate for the fundamental solution of a parabolic operator with piecewise smooth coefficients. Both gradient estimates are independent of the distances between manifolds of discontinuities.

  10. Two parabolic equations for propagation in layered poro-elastic media.

    Science.gov (United States)

    Metzler, Adam M; Siegmann, William L; Collins, Michael D; Collis, Jon M

    2013-07-01

    Parabolic equation methods for fluid and elastic media are extended to layered poro-elastic media, including some shallow-water sediments. A previous parabolic equation solution for one model of range-independent poro-elastic media [Collins et al., J. Acoust. Soc. Am. 98, 1645-1656 (1995)] does not produce accurate solutions for environments with multiple poro-elastic layers. First, a dependent-variable formulation for parabolic equations used with elastic media is generalized to layered poro-elastic media. An improvement in accuracy is obtained using a second dependent-variable formulation that conserves dependent variables across interfaces between horizontally stratified layers. Furthermore, this formulation expresses conditions at interfaces using no depth derivatives higher than first order. This feature should aid in treating range dependence because convenient matching across interfaces is possible with discretized derivatives of first order in contrast to second order.

  11. Increasing Powers in a Degenerate Parabolic Logistic Equation

    Institute of Scientific and Technical Information of China (English)

    José Francisco RODRIGUES; Hugo TAVARES

    2013-01-01

    The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem (O)tu-△u =au-b(x)up inΩ×R+,u(0)=u0,u(t)│(o)Ω =0,as p → +∞,where Ω is a bounded domain,and b(x) is a nonnegative function.The authors deduce that the limiting configuration solves a parabolic obstacle problem,and afterwards fully describe its long time behavior.

  12. Partition of Unity for a Class of Nonlinear Parabolic Equation on Overlapping Non-Matching Grids

    Institute of Scientific and Technical Information of China (English)

    Qisheng Wang; Kang Deng; Zhiguang Xiong; Yunqing Huang

    2007-01-01

    A class of nonlinear parabolic equation on a polygonal domain Ω ( ) R2 is investigated in this paper. We introduce a finite element method on overlapping non-matching grids for the nonlinear parabolic equation based on the partition of unity method. We give the construction and convergence analysis for the semi-discrete and the fully discrete finite element methods. Moreover, we prove that the error of the discrete variational problem has good approximation properties. Our results are valid for any spatial dimensions. A numerical example to illustrate the theoretical results is also given.

  13. Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

    Institute of Scientific and Technical Information of China (English)

    Chun-fa Li; Xue Yang; En-min Feng

    2008-01-01

    In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.

  14. Asymptotic Weighted-Periodicity of the Impulsive Parabolic Equation with Time Delay

    Institute of Scientific and Technical Information of China (English)

    Jin-liang Wang; Hui-feng Li

    2007-01-01

    The main aim of this paper is to investigate the effects of the impulse and time delay on a type of parabolic equations. In view of the characteristics of the equation, a particular iteration scheme is adopted.The results show that Under certain conditions on the coefficients of the equation and the impulse, the solution oscillates in a particular manner-called "asymptotic weighted-periodicity".

  15. Classification of heteroclinic orbits of semilinear parabolic equations with a polynomial nonlinearity

    Directory of Open Access Journals (Sweden)

    Michael Robinson

    2011-05-01

    Full Text Available For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain class of these equations, we show that some of the solutions which do not blow up actually tend to equilibria. The characterizing property of such solutions is a finite energy constraint, which comes about from the fact that this class of equations can be written as the flow of the L^2 gradient of a certain functional.

  16. Blow-up estimates for semilinear parabolic systems coupled in an equation and a boundary condition

    Institute of Scientific and Technical Information of China (English)

    WANG; Mingxin(

    2001-01-01

    [1]Wang, S., Wang, M. X., Xie, C. H., Reaction-diffusion systems with nonlinear boundary conditions, Z. angew. Math.Phys., 1997, 48(6): 994-1001.[2]Fila, M., Quittner, P., The blow-up rate for a semilinear parabolic system, J. Math. Anal. Appl., 1999, 238: 468-476.[3]Hu, B., Remarks on the blow-up estimate for solutions of the heat equation with a nonlinear boundary condition, Differential Integral Equations, 1996, 9(5): 891-901.[4]Hu, B. , Yin, H. M., The profile near blow-up time for solution of the heat equation with a nonlinear boundary condition,Trans. of Amer. Math. Soc., 1994, 346: 117-135.[5]Amann, H., Parabolic equations and nonlinear boundary conditions, J. of Diff. Eqns., 1988, 72: 201-269.[6]Deng, K., Blow-up rates for parabolic systems, Z. angew. Math. Phys. ,1996, 47: 132-143.[7]Fila, M., Levine, H. A., On critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition, J. Math. Anal. Appl., 1996, 204: 494-521.

  17. Parabolic equations and Feynman_Kac formula on general bounded domains

    Institute of Scientific and Technical Information of China (English)

    ZHANG; Gongqing

    2001-01-01

    [1]Berestycki, H., Nirenberg, L., Varadhan, S. V. R., The principal eigenvalue and maximum principle for second order elliptic operators in general domains, Comm. Pure and Appl. Math., 1994, 47: 47.[2]Chen, Y. Z., Alexandrov's maximum principle and Bony's maximum principle for parabolic equations, Acta Mathematica Applicae Sinica, 1985, 2: 309.[3]Dong, G. C., Nonlinear Second Order Partial Differential Equations, AMS Translations, Providence: AMS, 1991.[4]Krylov, N. V., Nonlinear Elliptic and Parabolic Equations of Second Order, Mathematics and Its Applications, Dordrecht: D. Reidel Publication Company, 1987.[5]Tso, K. S., On the Alexandrov_Bakel'man type maximum principle for second order parabolic equations, Comm. PDE, 1985, 10: 543.[6]Miller, K., Barriers on cones for uniformly elliptic operators, Ann. Mat. Pura e Appl., 1967, 76: 93.[7]Strook, D., Varadhan, S. V. R., Multidimensional Diffusion Process, New York, Berlin: Springer_Verlag, 1979.[8]Pinsky, R. G., Positive Harmonic Functions and Diffusions, Cambridge: Cambridge University Press, 1995.[9]Friedman, A., Partial Differential Equations of Parabolic Type, Englewood Cliffs: Prentice_Hall Inc., 1964.

  18. Blow-up theories for semilinear parabolic equations

    CERN Document Server

    Hu, Bei

    2011-01-01

    There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.

  19. About one special boundary value problem for multidimensional parabolic integro-differential equation

    Science.gov (United States)

    Khairullin, Ermek

    2016-08-01

    In this paper we consider a special boundary value problem for multidimensional parabolic integro-differential equation with boundary conditions that contains as a boundary condition containing derivatives of order higher than the order of the equation. The solution is sought in the form of a thermal potential of a double layer. Shows lemma of finding the limits of the derivatives of the unknown function in the neighborhood of the hyperplane. Using the boundary condition and lemma obtained integral-differential equation (IDE) of parabolic operators, whĐţre an unknown function under the integral contains higher-order space variables derivatives. IDE is reduced to a singular integral equation (SIE), when an unknown function in the spatial variables satisfies the Holder. The characteristic part is solved in the class of distribution function using method of transformation of Fourier-Laplace. Found an algebraic condition for the transition to the classical generalized solution. Integral equation of the resolvent for the characteristic part of SIE is obtained. Integro-differential equation is reduced to the Volterra-Fredholm type integral equation of the second kind by method of regularization. It is shown that the solution of SIE is a solution of IDE. Obtain a theorem on the solvability of the boundary value problem of multidimensional parabolic integro-differential equation, when a known function of the spatial variables belongs to the Holder class and satisfies the solvability conditions.

  20. MULTISCALE ASYMPTOTIC EXPANSION FOR A CLASS OF HYPERBOLIC-PARABOLIC TYPE EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Li-qun Cao; De-chao Zhu; Jian-Lan Luo

    2002-01-01

    In this paper, we will discuss the asymptotic behaviour for a class of hyper bolic -parabolic type equation with highly oscillatory coefficients arising from the strong-transient heat and mass transfer problems of composite media. A complete multiscale asymptotic expansion and its rigorous verification will be reported.

  1. The asymptotics of a solution of a parabolic equation as time increases without bound

    Energy Technology Data Exchange (ETDEWEB)

    Degtyarev, Denis O; Il' in, Arlen M

    2012-11-30

    A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of t{sup -1} is constructed and substantiated. Bibliography: 8 titles.

  2. The problem with inclined derivative for a parabolic equations with impulse conditions and degeneration

    Directory of Open Access Journals (Sweden)

    I. D. Pukalskiy

    2014-12-01

    Full Text Available By application of maximum principle and apriori estimates it is studied the inclined derivative problem for a linear parabolic equation with power singularity in the coefficients with respect to space variables and impulse conditions respect to time variable. It is established the uniqueness and the existence of the solution of the stated problem in Holder spaces.

  3. Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    LIU Yang; FENG Hui

    2005-01-01

    The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.

  4. STABILIZED NUMERICAL APPROXIMATIONS OF THE BACKWARD PROBLEM OF A PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    韩厚德; 胡刚

    2001-01-01

    In this paper, the backward problem ora parabolic equation is considered. Three new stability estimates are given. Based on the new stability estimates, a regularization method is proposed for which error estimates are available. The regularization method can be used for the numerical approximations of the original problem which will be shown by the numerical examples.

  5. Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term

    Directory of Open Access Journals (Sweden)

    Huilai Li

    2015-12-01

    Full Text Available This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at infinity.

  6. Semilinear Parabolic Equations on the Heisenberg Group with a Singular Potential

    Directory of Open Access Journals (Sweden)

    Houda Mokrani

    2012-01-01

    Full Text Available We discuss the asymptotic behavior of solutions for semilinear parabolic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy's inequality, and the nonlinearity is controlled by Sobolev's inequality. We also establish the existence of a global branch of the corresponding steady states via the classical Rabinowitz theorem.

  7. Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

    Science.gov (United States)

    2010-09-01

    and Schrödinger’s equation in (2 1) dimensions,” J. Phys. A: Math. Gen., vol. 30, pp. 819–830, 1997. [13] J. S. Papadakis , P. Taroudakis, P. J... Papadakis , and B. Mayfield, “A new method for a realistic treatment of the sea bottom in the parabolic approximation,” J. Acoust. Soc. Amer., vol. 92, no

  8. THE FINITE ELEMENT METHODS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Error estimates are established for the finite dement methods to solve a class of second or der nonlinear parabolic equations. Optimal rates of convergence in L2-and H1-norms are derived. Meanwhile,the schenes are second order correct in time.

  9. SEMIDISCRETIZATION IN SPACE OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS WITH BLOW-UP OF THE SOLUTIONS

    Institute of Scientific and Technical Information of China (English)

    Tetsuya Ishiwata; Masayoshi Tsutsumi

    2000-01-01

    Semidiscretization in space of nonlinear degenerate parabolic equations of nondivergent form is presented, under zero Dirichlet boundary condition. It is shown that semidiscrete solutions blow up in finite time. In particular, the asymptotic behavior of blowing-up solutions, is discussed precisely.

  10. Strong and Weak Property of Travelling Wave Front Solutions for a Class of Degenerate Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    LI Zheng-yuan; LIU Ying-dong; YE Qi-xiao

    2001-01-01

    In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction-diffusion terms are showed.

  11. THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    N'guimbi; Germain

    2001-01-01

    Abstract. The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal Lz and H1 estimates for the error and its time derivative are established.

  12. Global Existence and Blowup for a Parabolic Equation with a Non-Local Source and Absorption

    DEFF Research Database (Denmark)

    Ling, Zhi; Lin, Zhigui; Pedersen, Michael

    2013-01-01

    In this paper we consider a double fronts free boundary problem for a parabolic equation with a non-local source and absorption. The long time behaviors of the solutions are given and the properties of the free boundaries are discussed. Our results show that if the initial value is sufficiently...

  13. Galerkin. methods for even-order parabolic. equations in one space variable

    NARCIS (Netherlands)

    Bakker, M.

    1982-01-01

    For parabolic equations in one space variable with a strongly coercive self-adjoint $2m$th order spatial operator, a $k$th degree Faedo-Galerkin method is developed which has local convergence of order $2(k + 1 - m)$ at the knots for the first $m - 1$ spatial derivatives and, if $k \\geqq 2m$, conver

  14. Analysis of the linear stability of compressible boundary layers using the PSE. [parabolic stability equations

    Science.gov (United States)

    Bertolotti, F. P.; Herbert, TH.

    1991-01-01

    The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.

  15. Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form

    Directory of Open Access Journals (Sweden)

    Kairi Kasemets

    2013-01-01

    Full Text Available We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.

  16. Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria

    Science.gov (United States)

    Figueroa-López, R. N.; Lozada-Cruz, G.

    2016-11-01

    In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.

  17. TOTAL VERSUS SINGLE POINT BLOW-UP SOLUTIONS FOR A SEMILINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    Yang Ming

    2007-01-01

    In this paper, we investigate the blow-up set of solutions of a parabolic equation with localized and non-localized reactions. We completely classify blow-up solutions into total blow-up cases and single point blow-up cases.

  18. Problem with two-point conditions for parabolic equation of second order on time

    Directory of Open Access Journals (Sweden)

    M. M. Symotyuk

    2014-12-01

    Full Text Available The  correctness of a problem with two-point conditions ontime-variable and of  Dirichlet-type conditions  on spatialcoordinates for the linear  parabolic equations with variablecoefficients are established. The metric theorem on estimationsfrom below of small denominators of the problem (the notions of Hausdorff measure is proved.

  19. Optimal control for systems governed by parabolic equations without initial conditions with controls in the coefficients

    Directory of Open Access Journals (Sweden)

    Mykola Bokalo

    2017-03-01

    Full Text Available We consider an optimal control problem for systems described by a Fourier problem for parabolic equations. We prove the existence of solutions, and obtain necessary conditions of the optimal control in the case of final observation when the control functions occur in the coefficients.

  20. Error estimates for finite element solution for parabolic integro-differential equations

    Directory of Open Access Journals (Sweden)

    Hasan N. Ymeri

    1993-05-01

    Full Text Available In this paper we first study the stability of Ritz-Volterra projection and its maximum norm estimates, and then we use these results to derive some L\\infty error estimates for finite element methods for parabolic partial integro-differential equations.

  1. Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    [1]Oleinik, O. A., Samokhin,V. N., Mathematical Models in Boundary Layer Theorem, Boca Raton; Chapman and Hall/CRC, 1999.[2]Volpert, A.I., Hudjaev, S.I., On the problem for quasilinear degenerate parabolic equations of second order(Russian), Mat. Sb., 1967, 3: 374-396.[3]Zhao, J., Uniqueness of solutions of quasilinear degenerate parabolic equations, Northeastern Math. J., 1985,1(2): 153-165.[4]Wu, Z., Yin, J., Some properties of functions in BVx and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations, Northeastern Math. J., 1989,5(4): 395-422.[5]Brezis, H., Crandall, M.G., Uniqueness of solutions of the initial value problem for ut- △ψ(u) = 0, J.Math. Pures et Appl., 1979, 58: 153-163.[6]Kruzkov, S.N., First order quasilinear equations in several independent varaiables, Math. USSR-Sb., 1970, 10:217-243.[7]Cockburn, B., Gripenberg, G., Continious dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Diff. Equatiaons, 1999, 151: 231-251.[8]Volpert, A.I., BV space and quasilinear equations, Mat. Sb., 1967, 73: 255-302.[9]Volpert, A.I., Hudjave, S.I., Analysis of class of discontinuous functions and the equations of mathematical physics (Russian), Izda. Nauka Moskwa, 1975.[10]Evans, L.C., Weak convergence methods for nonlinear partial differential equations, Conference Board of the Mathematical Sciences, Regional Conferences Series in Mathematics Number 74, 1998.[11]Wu, Z., Zhao, J., Yin, J., et al., Nonlinear Diffusion Equations, Singapore: Word Scientific, 2001.

  2. Long-term Analysis of Degenerate Parabolic Equations in RN

    Institute of Scientific and Technical Information of China (English)

    Gao Cheng YUE; Cheng Kui ZHONG

    2015-01-01

    Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using ?-trajectories methods, we proved that weak solutions generated by degenerate equations possess an (L2U (RN ), L2loc(RN ))-global attractor. Moreover, the upper bounds of the Kolmogorovε-entropy for such global attractor are also obtained.

  3. Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

    KAUST Repository

    Lorz, Alexander

    2011-01-17

    Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.

  4. Dirac mass dynamics in a multidimensional nonlocal parabolic equation

    CERN Document Server

    Lorz, Alexander; Perthame, Benoit

    2010-01-01

    Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses co-exist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a structure of gradient flow. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models darwinian evolution.

  5. A POSTERIORI ERROR ESTIMATE FOR BOUNDARY CONTROL PROBLEMS GOVERNED BY THE PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Wei Gong; Ningning Yan

    2009-01-01

    In this paper.we discuss the a posteriori error estimate of the finite element approximation for the boundary control problems governed by the parabolic partial differential equations.Three different a posteriori error estimators are provided for the parabolic boundary control problems with the observations of the distributed state.the boundary state and the final state.It is proven that these estimators are reliable bounds of the finite element approximation errors,which can be used as the indicators of the mesh refinement in adaptive finite element methods.

  6. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

    Directory of Open Access Journals (Sweden)

    M. G. Crandall

    1999-07-01

    Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

  7. Calculation of Wave Radiation Stress in Combination with Parabolic Mild Slope Equation

    Institute of Scientific and Technical Information of China (English)

    ZHENG Yonghong; SHEN Yongming; QIU Dahong

    2000-01-01

    A new method for the calculation of wave radiation stress is proposed by linking the expressions for wave radiation stress with the variables in the parabolic mild slope equation. The governing equations are solved numerically by the finite difference method. Numerical results show that the new method is accurate enough, can be efficiently solved with little programming effort, and can be applied to the calculation of wave radiation stress for large coastal areas.

  8. Hoelder Continuity for Solutions of Degenerate Parabolic Equation with Two Degenerate Points

    Institute of Scientific and Technical Information of China (English)

    刘建中; 李育生; 等

    1993-01-01

    In this paper we discuss the quasilinear parabolic equation Ut=△↓(uα(1-u)β.△↓u)+B(x,t,u)△↓u+C(x,t,u)which is degenerate at u=0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0

  9. An approximate Riemann solver for real gas parabolized Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Urbano, Annafederica, E-mail: annafederica.urbano@uniroma1.it [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy); Nasuti, Francesco, E-mail: francesco.nasuti@uniroma1.it [Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Universita di Roma, Via Eudossiana 18, Roma 00184 (Italy)

    2013-01-15

    Under specific assumptions, parabolized Navier-Stokes equations are a suitable mean to study channel flows. A special case is that of high pressure flow of real gases in cooling channels where large crosswise gradients of thermophysical properties occur. To solve the parabolized Navier-Stokes equations by a space marching approach, the hyperbolicity of the system of governing equations is obtained, even for very low Mach number flow, by recasting equations such that the streamwise pressure gradient is considered as a source term. For this system of equations an approximate Roe's Riemann solver is developed as the core of a Godunov type finite volume algorithm. The properties of the approximated Riemann solver, which is a modification of Roe's Riemann solver for the parabolized Navier-Stokes equations, are presented and discussed with emphasis given to its original features introduced to handle fluids governed by a generic real gas EoS. Sample solutions are obtained for low Mach number high compressible flows of transcritical methane, heated in straight long channels, to prove the solver ability to describe flows dominated by complex thermodynamic phenomena.

  10. A new explicit method for the numerical solution of parabolic differential equations

    Science.gov (United States)

    Satofuka, N.

    1983-01-01

    A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.

  11. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  12. Exact transparent boundary conditions for the parabolic wave equations with linear and quadratic potentials

    CERN Document Server

    Feshchenko, R M

    2016-01-01

    In this paper exact 1D transparent boundary conditions (TBC) for the 2D parabolic wave equation with a linear or a quadratic dependence of the dielectric permittivity on the transversal coordinate are reported. Unlike the previously derived TBCs they contain only elementary functions. The obtained boundary conditions can be used to numerically solve the 2D parabolic equation describing the propagation of light in weakly bent optical waveguides and fibers including waveguides with variable curvature. They also are useful when solving the equivalent 1D Schr\\"odinger equation with a potential depending linearly or quadratically on the coordinate. The prospects and problems of discretization of the derived transparent boundary conditions are discussed.

  13. Existence of extremal periodic solutions for quasilinear parabolic equations

    Directory of Open Access Journals (Sweden)

    Siegfried Carl

    1997-01-01

    bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.

  14. Klein geometries, parabolic geometries and differential equations of finite type

    CERN Document Server

    Abadoglu, Ender

    2009-01-01

    We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).

  15. A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Zhendong LUO; Lei LI; Ping SUN

    2013-01-01

    In this paper, we extend the applications of proper orthogonal decomposition (POD) method, i.e., apply POD method to a mixed finite element (MFE) formulation naturally satisfied Brezz-Babu˘ska for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis-tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

  16. On the Uniqueness and Stability of Entropy Solutions of nonlinear degenerate parabolic Equations with rough Coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendahl; Risebro, Nils Henrik

    2000-05-01

    This paper studies nonlinear degenerate parabolic equations where the flux function does not depend Lipshitz continuously on the spatial position x. By properly adapting the 'doubling of variable' device due to Kruzkov and Carrillo, the authors prove a uniqueness result within the class of entropy solutions for the initial value problem. They also prove a result concerning the continuous dependence on the initial data and the flux function for degenerate parabolic equations with flux function of the form k(x)f(u), where k(x) is a vector-valued function and f(u) is a scalar function of the unknown scalar function u(x,t) which is sought.

  17. Treatment of ice cover and other thin elastic layers with the parabolic equation method.

    Science.gov (United States)

    Collins, Michael D

    2015-03-01

    The parabolic equation method is extended to handle problems involving ice cover and other thin elastic layers. Parabolic equation solutions are based on rational approximations that are designed using accuracy constraints to ensure that the propagating modes are handled properly and stability constrains to ensure that the non-propagating modes are annihilated. The non-propagating modes are especially problematic for problems involving thin elastic layers. It is demonstrated that stable results may be obtained for such problems by using rotated rational approximations [Milinazzo, Zala, and Brooke, J. Acoust. Soc. Am. 101, 760-766 (1997)] and generalizations of these approximations. The approach is applied to problems involving ice cover with variable thickness and sediment layers that taper to zero thickness.

  18. Parabolic equations in biology growth, reaction, movement and diffusion

    CERN Document Server

    Perthame, Benoît

    2015-01-01

    This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

  19. On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem

    Directory of Open Access Journals (Sweden)

    M. Denche

    1999-01-01

    Full Text Available In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The results obtained are then applied to the study of a nonlocal parabolic transmission problem.

  20. Outdoor Sound Propagation Modelling in Complex Environments: Recent Developments in the Parabolic Equation Method

    Science.gov (United States)

    2006-10-01

    equation for sound waves in inhomogeneous moving media”, Acustica united with Acta Acustica , Vol 83(3), pp 455-460,1997. [3] L. Dallois, Ph. Blanc...propagation in a turbulent atmosphere within the parabolic approximation”, Acustica united with Acta Acustica , Vol 87(1), pp 659-669, 2001 [6] M. Karweit...approaches", Acta Acustica united with Acustica , 89 (6), 980-991, (2003). [40] Ph. Voisin, Ph. Blanc-Benon, "The influence of meteorological

  1. The BV solution of the parabolic equation with degeneracy on the boundary

    Directory of Open Access Journals (Sweden)

    Zhan Huashui

    2016-12-01

    Full Text Available Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.

  2. Mixed Problem with an Integral Two-Space-Variables condition for a Third Order Parabolic Equation

    Directory of Open Access Journals (Sweden)

    Oussaeif Taki Eddine

    2016-10-01

    Full Text Available This paper is concerned with the existence and uniqueness of a strong solution to a mixed problem which combine Dirichlet and integral two space variables conditions for a third order linear parabolic equation. The proof uses a functional analysis method presented, which it is based on an energy inequality and the density of the range of the operator generated by the problem.

  3. Obstacle problem for a class of parabolic equations of generalized p-Laplacian type

    Science.gov (United States)

    Lindfors, Casimir

    2016-11-01

    We study nonlinear parabolic PDEs with Orlicz-type growth conditions. The main result gives the existence of a unique solution to the obstacle problem related to these equations. To achieve this we show the boundedness of weak solutions and that a uniformly bounded sequence of weak supersolutions converges to a weak supersolution. Moreover, we prove that if the obstacle is continuous, so is the solution.

  4. POINTWISE CONVERGENCE OF THE WAVELET SOLUTION TO THE PARABOLIC EQUATION WITH VARIABLE COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Jinru Wang; Hua Zhang

    2008-01-01

    We consider the parabolic equation with variable coefficients k(x)uxx = ui, O,x ≤ 1, t ≥ 0, where 0 < a ≤ k(x) < +∞, the solution on the boundary x = O is a given function g and ux(O,t) = O. We use wavelet Galerkin method with Meyer multi-resolution analy-sis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.

  5. On a third order parabolic equation with a nonlocal boundary condition

    Directory of Open Access Journals (Sweden)

    Abdelfatah Bouziani

    2000-01-01

    Full Text Available In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.

  6. Self-similar singular solution of doubly singular parabolic equation with gradient absorption term

    Directory of Open Access Journals (Sweden)

    Shi Peihu

    2006-01-01

    Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for , and in . By shooting and phase plane methods, we prove that when there exists self-similar singular solution, while there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.

  7. Finite element formulation based on proper orthogonal decomposition for parabolic equations

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    A proper orthogonal decomposition (POD) method is applied to a usual finite element (FE) formulation for parabolic equations so that it is reduced into a POD FE formulation with lower dimensions and enough high accuracy. The errors between the reduced POD FE solution and the usual FE solution are analyzed. It is shown by numerical examples that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is also shown that this validates the feasibility and efficiency of POD method.

  8. On asymptotic time decay of solutions to a parabolic equation in unbounded domains

    Directory of Open Access Journals (Sweden)

    P. Maremonti

    1991-05-01

    Full Text Available Estimates on the asymptotic behaviour of solutions to a parabolic equation are given, when the I.B.V.P. is posed in particular domains. More precisely, the domain Ω is unbounded, unbounded in any direction, and Ω is enclosed in a wedge or in a cone of two or three-dimensional Euclidean space. It is proved that the order of decay is increasing for decreasing opening of the wedge or of the cone.

  9. Application of the Beilis-Tappert parabolic equation method to sound propagation over irregular terrain.

    Science.gov (United States)

    Parakkal, Santosh; Gilbert, Kenneth E; Di, Xiao

    2012-02-01

    The Beilis-Tappert (1979) parabolic equation method is attractive for irregular terrain because it treats surface variations in terms of a simple multiplicative factor ("phase screen"). However, implementing the exact sloping-surface impedance condition is problematic if one wants the computational efficiency of a Fourier parabolic equation algorithm. This article investigates an approximate flat-ground impedance condition that allows the Beilis-Tappert phase screen method to be used with a Fourier algorithm without any added complications. The exact sloping-surface impedance condition is derived and applied to propagation predictions over hills with maximum slopes from 5° to 22°. The predictions with the exact impedance condition are compared to predictions using the approximate flat-ground impedance condition. It is found that for slopes less than 15°-20°, the flat-ground impedance condition is sufficiently accurate. For slopes greater than approximately 20°, the limiting factor on numerical accuracy is not the flat-ground impedance approximation, but rather the narrow-angle approximation required by the Beilis-Tappert method. Thus, within the 20° limitation and using the flat-ground impedance condition with a Fourier parabolic equation, sound propagation over irregular terrain can be computed simply, efficiently, and accurately.

  10. An H1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

    Directory of Open Access Journals (Sweden)

    A. K. Pani

    1987-01-01

    Full Text Available Optimal error estimates in L2, H1 and H2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an H1-Galerkin procedure.

  11. Homogenization of a singularly perturbed degenerated parabolic equation and application to seabed dune and megaripple morphodynamics in tided environment

    CERN Document Server

    Faye, Ibrahima; Seck, Diaraf

    2009-01-01

    In this paper we build models for short-term, mean-term and long-term dynamics of dune and megariple morphodynamics. They are models that are degenerated parabolic equations which are, moreover, singularly perturbed. We, then give an existence and uniqueness result for the short-term and mean-term models. This result is based on a time-space periodic solution existence result for degenerated parabolic equation that we set out. Finally the short-term model is homogenized.

  12. OPTIMAL ESTIMATES FOR THE SEMIDISCRETE GALERKIN METHOD APPLIED TO PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH DATA

    KAUST Repository

    GOSWAMI, DEEPJYOTI

    2014-01-01

    AWe propose and analyse an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time-dependent parabolic integro-differential equation with nonsmooth initial data. The method is based on energy arguments combined with repeated use of time integration, but without using parabolic-type duality techniques. An optimal L2-error estimate is derived for the semidiscrete approximation when the initial data is in L2. A superconvergence result is obtained and then used to prove a maximum norm estimate for parabolic integro-differential equations defined on a two-dimensional bounded domain. © 2014 Australian Mathematical Society.

  13. Critical Blow-Up and Global Existence for Discrete Nonlinear p-Laplacian Parabolic Equations

    Directory of Open Access Journals (Sweden)

    Soon-Yeong Chung

    2014-01-01

    Full Text Available The goal of this paper is to investigate the blow-up and the global existence of the solutions to the discrete p-Laplacian parabolic equation utx,t=Δp,wux,t+λux,tp-2ux,t, x,t∈S×0,∞, ux,t=0, x,t∈∂S×0,∞, ux,0=u0, depending on the parameters p>1 and λ>0. Besides, we provide several types of the comparison principles to this equation, which play a key role in the proof of the main theorems. In addition, we finally give some numerical examples which exploit the main results.

  14. Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations (Ⅱ)

    Institute of Scientific and Technical Information of China (English)

    WU Hai-jun; LI Rong-hua

    2001-01-01

    In this article we extend ours framework of long-time convergence for numeracal approximations of semilinear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J., 16(1)(2000), 1-28”, to the Gauss-Ledendre full discretization. When apply the result to the CrankNicholson finiteelement full diseretization of the Navier-Stokes equations, we can remore the grid-ratio restriction of“Heywood, J. G. and Rannacher, R., SIAM J. Numer. Anal., 27(1990), 353-384”,and weaken the stability condition on the continuous solution.

  15. Solving parabolic and hyperbolic equations by the generalized finite difference method

    Science.gov (United States)

    Benito, J. J.; Urena, F.; Gavete, L.

    2007-12-01

    Classical finite difference schemes are in wide use today for approximately solving partial differential equations of mathematical physics. An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method, that can be applied to irregular grids of points. In this paper the extension of the GFD to the explicit solution of parabolic and hyperbolic equations has been developed for partial differential equations with constant coefficients in the cases of considering one, two or three space dimensions. The convergence of the method has been studied and the truncation errors over irregular grids are given. Different examples have been solved using the explicit finite difference formulae and the criterion of stability. This has been expressed in function of the coefficients of the star equation for irregular clouds of nodes in one, two or three space dimensions. The numerical results show the accuracy obtained over irregular grids. This paper also includes the study of the maximum local error and the global error for different examples of parabolic and hyperbolic time-dependent equations.

  16. Recent results and open problems on parabolic equations with gradient nonlinearities

    Directory of Open Access Journals (Sweden)

    Philippe Souplet

    2001-03-01

    Full Text Available We survey recent results and present a number of open problems concerning the large-time behavior of solutions of semilinear parabolic equations with gradient nonlinearities. We focus on the model equation with a dissipative gradient term $$u_t-Delta u=u^p-b|abla u|^q,$$ where $p$, $q>1$, $b>0$, with homogeneous Dirichlet boundary conditions. Numerous papers were devoted to this equation in the last ten years, and we compare the results with those known for the case of the pure power reaction-diffusion equation ($b=0$. In presence of the dissipative gradient term a number of new phenomena appear which do not occur when $b=0$. The questions treated concern: sufficient conditions for blowup, behavior of blowing up solutions, global existence and stability, unbounded global solutions, critical exponents, and stationary states.

  17. Energy Equations for Computation of Parabolic-Trough Collector Efficiency Using Solar Position Coordinates

    Directory of Open Access Journals (Sweden)

    I. S. Sintali

    2014-10-01

    Full Text Available This paper presents the development of energy equations for computation of the efficiency of Parabolic-Trough Collector (PTC using solar coordinates. The energy equations included the universal time , day (n, month (M, year (Y, delta T llongitude and latitude in radian. The heliocentric longitude (H, geocentric global coordinates and local topocentric sun coordinates were considered in the modeling equations. The thermal efficiency of the PTC considered both the direct and reflected solar energy incident on the glass-cover as well as the thermal properties of the collector and the total energy losses in the system. The developed energy equations can be used to predict the performance (efficiency of any PTC using the meteorological and radiative data of any particular location.

  18. A relaxation technique for the parabolized Navier-Stokes (PNS) equations

    Science.gov (United States)

    Kaul, Upender K.

    1986-01-01

    A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

  19. Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

    CERN Document Server

    Imbert, Cyril

    2009-01-01

    The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic i...

  20. Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

    Directory of Open Access Journals (Sweden)

    Pan Zheng

    2012-01-01

    Full Text Available We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul+uq,  (x,t∈RN×(0,T, where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.

  1. Optimal Three Cylinder Inequality at the Boundary for Solutions to Parabolic Equations and Unique Continuation Properties

    Institute of Scientific and Technical Information of China (English)

    Sergio VESSELLA

    2005-01-01

    Let Г be a portion of a C1,α boundary of an n-dimensional domain D. Let u be a solution to a second order parabolic equation in D × (-T,T) and assume that u = 0 on Г× (-T,T), 0 ∈Г. We result we prove that if u (x,t) = O (|x|k) for every t ∈ (-T,T) and every k ∈ N, then u is identically equal to zero.

  2. Existence and regularity of a global attractor for doubly nonlinear parabolic equations

    Directory of Open Access Journals (Sweden)

    Abderrahmane El Hachimi

    2002-05-01

    Full Text Available In this paper we consider a doubly nonlinear parabolic partial differential equation $$ frac{partial eta (u}{partial t}-Delta _{p}u+f(x,t,u=0 quad hbox{in }Omega imesmathbb{R}^{+}, $$ with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities $Beta$, $f$, and on $p$, we prove more regularity for the global attractor and obtain stabilization results for the solutions.

  3. Stability results for backward parabolic equations with time-dependent coefficients

    Science.gov (United States)

    Nho Hào, Dinh; Van Duc, Nguyen

    2011-02-01

    Let H be a Hilbert space with the norm || sdot || and A(t) (0 Dokl. Akad. Nauk SSSR 114 1162-5), and Agmon and Nirenberg (1963 Commun. Pure Appl. Math. 16 121-239). Our regularization method with a priori and a posteriori parameter choice yields error estimates of Hölder type. This is the only result when a regularization method for backward parabolic equations with time-dependent coefficients provides a convergence rate. Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th birthday.

  4. Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    Tongke

    2010-01-01

    This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

  5. Existence results for a class of parabolic evolution equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    WangJing; XueXingmei

    2003-01-01

    We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.

  6. Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

    Directory of Open Access Journals (Sweden)

    Tan Qi-Jian

    2011-01-01

    Full Text Available Abstract This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global piecewise classical solutions under certain conditions including mixed quasimonotone property of reaction functions. Applications are given to three 2-species Volterra-Lotka models with discontinuous coefficients and continuous delays.

  7. On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations

    Directory of Open Access Journals (Sweden)

    Helge Holden

    2003-04-01

    Full Text Available We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general $L^p$ compactness criterion. The uniqueness proof is an adaption of Kruzkov's ``doubling of variables'' proof. We also present a numerical example motivated by biodegradation in porous media.

  8. Stabilization of the solution of a doubly nonlinear parabolic equation

    Energy Technology Data Exchange (ETDEWEB)

    Andriyanova, È R [Ufa State Aviation Technical University, Ufa (Russian Federation); Mukminov, F Kh [Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa (Russian Federation)

    2013-09-30

    The method of Galerkin approximations is employed to prove the existence of a strong global (in time) solution of a doubly nonlinear parabolic equation in an unbounded domain. The second integral identity is established for Galerkin approximations, and passing to the limit in it an estimate for the decay rate of the norm of the solution from below is obtained. The estimates characterizing the decay rate of the solution as x→∞ obtained here are used to derive an upper bound for the decay rate of the solution with respect to time; the resulting estimate is pretty close to the lower one. Bibliography: 17 titles.

  9. Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆

    Directory of Open Access Journals (Sweden)

    Rubio Gerardo

    2011-03-01

    Full Text Available We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem. Nous considérons le problème de Cauchy dans ℝd pour une classe d’équations aux dérivées partielles paraboliques semi linéaires qui se pose dans certains problèmes de contrôle stochastique. Nous supposons que les coefficients ne sont pas bornés et sont localement Lipschitziennes, pas nécessairement différentiables, avec des données continues et ellipticité local uniforme. Nous construisons une solution classique par approximation avec les équations paraboliques linéaires. Les équations linéaires impliquées ne peuvent être résolues avec les résultats traditionnels. Par conséquent, nous construisons une solution classique au problème de Cauchy linéaire sous les mêmes hypothèses sur les coefficients pour l’équation semi-linéaire. Notre approche utilise les équations différentielles stochastiques et les équations différentielles paraboliques dans les domaines bornés. Enfin, nous appliquons les résultats à un problème stochastique de consommation optimale.

  10. The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations

    Institute of Scientific and Technical Information of China (English)

    Lü BO-QIANG; LI FENG-QUAN

    2012-01-01

    For the more general parabolic Monge-Ampère equations defined by the operator F(D2u + σ(x)),the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equation are established.A new structure condition which is used to get a priori estimate is established.

  11. A necessary and sufficient condition for finite speed of propagation in the theory of doubly nonlinear degenerate parabolic equations

    NARCIS (Netherlands)

    Gilding, B.H.; Kersner, R.

    1996-01-01

    A degenerate parabolic partial differential equation with a time derivative and first- and second-order derivatives with respect to one spatial variable is studied. The coefficients in the equation depend nonlinearly on both the unknown and the first spatial derivative of a function of the unknown.

  12. Perfectly matched layer for an elastic parabolic equation model in ocean acoustics

    Science.gov (United States)

    Xu, Chuanxiu; Zhang, Haigang; Piao, Shengchun; Yang, Shi'e.; Sun, Sipeng; Tang, Jun

    2017-02-01

    The perfectly matched layer (PML) is an effective technique for truncating unbounded domains with minimal spurious reflections. A fluid parabolic equation (PE) model applying PML technique was previously used to analyze the sound propagation problem in a range-dependent waveguide (Lu and Zhu, 2007). However, Lu and Zhu only considered a standard fluid PE to demonstrate the capability of the PML and did not take improved one-way models into consideration. They applied a [1/1] Padé approximant to the parabolic equation. The higher-order PEs are more accurate than standard ones when a very large angle propagation is considered. As for range-dependent problems, the techniques to handle the vertical interface between adjacent regions are mainly energy conserving and single-scattering. In this paper, the PML technique is generalized to the higher order elastic PE, as is to the higher order fluid PE. The correction of energy conserving is used in range-dependent waveguides. Simulation is made in both acoustic cases and seismo-acoustic cases. Range-independent and range-dependent waveguides are both adopted to test the accuracy and efficiency of this method. The numerical results illustrate that a PML is much more effective than an artificial absorbing layer (ABL) both in acoustic and seismo-acoustic sound propagation modeling.

  13. The numerical solution of the boundary inverse problem for a parabolic equation

    Science.gov (United States)

    Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.

    2016-10-01

    Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.

  14. Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

    Science.gov (United States)

    Frank, Scott D; Collis, Jon M; Odom, Robert I

    2015-06-01

    Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

  15. Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

    Directory of Open Access Journals (Sweden)

    Jian Wang

    2009-01-01

    Full Text Available We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: (|f′|p−2f′′+βrf′+αf+(fq′=0 satisfying a specific decay rate: lim⁡r→∞rα/βf(r=0 with α:=(p−1/(pq−2p+2 and β:=(q−p+1/(pq−2p+2. Here p>2 and q>p−1. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term ut=(|ux|p−2uxx+(uqx defined on the half line [0,+∞.

  16. Noniterative grid generation using parabolic difference equations for fuselage-wing flow calculations

    Science.gov (United States)

    Nakamura, S.

    1982-01-01

    A fast method for generating three-dimensional grids for fuselage-wing transonic flow calculations using parabolic difference equations is described. No iterative scheme is used in the three-dimensional sense; grids are generated from one grid surface to the next starting from the fuselage surface. The computational procedure is similar to the iterative solution of the two-dimensional heat conduction equation. The proposed method is at least 10 times faster than the elliptic grid generation method and has much smaller memory requirements. Results are presented for a fuselage and wing of NACA-0012 section and thickness ratio of 10 percent. Although only H-grids are demonstrated, the present technique should be applicable to C-grids and O-grids in three dimensions.

  17. Smoothness of semiflows for parabolic partial differential equations with state-dependent delay

    Science.gov (United States)

    Lv, Yunfei; Yuan, Rong; Pei, Yongzhen

    2016-04-01

    In this paper, the smoothness properties of semiflows on C1-solution submanifold of a parabolic partial differential equations with state-dependent delay are investigated. The problem is formulated as an abstract ordinary retarded functional differential equation of the form du (t) / dt = Au (t) + F (ut) with a continuously differentiable map G from an open subset U of the space C1 ([ - h , 0 ] ,L2 (Ω)), where A is the infinitesimal generator of a compact C0-semigroup. The present study is continuation of a previous work [14] that highlights the classical solutions and C1-smoothness of solution manifold. Here, we further prove the continuous differentiability of the semiflow. We finally verify all hypotheses by a biological example which describes a stage structured diffusive model where the delay, which is the time taken from birth to maturity, is assumed as a function of a immature species population.

  18. Holder continuity of bounded weak solutions to generalized parabolic p-Laplacian equations II: singular case

    Directory of Open Access Journals (Sweden)

    Sukjung Hwang

    2015-11-01

    Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1

  19. Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery.

    Science.gov (United States)

    Carasso, Alfred S

    2013-01-01

    Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.

  20. Regularity of weak solutions of elliptic and parabolic equations with some critical or supercritical potentials

    Science.gov (United States)

    Li, Zijin; Zhang, Qi S.

    2017-07-01

    We prove H\\"older continuity of weak solutions of the uniformly elliptic and parabolic equations %$\\Delta u-\\frac{A}{|x|^{2+\\beta}}u=0,\\,\\,(\\beta\\geq 0)$, and variable second order term coefficients case $%% \\begin{equation}\\label{01} \\partial_{i} (a_{ij}(x) \\partial_{j}u(x)) - \\frac{A}{|x|^{2+\\beta}} u(x) =0\\quad (A>0,\\quad\\beta\\geq 0), \\end{equation} \\begin{equation}\\label{02} \\partial_{i} (a_{ij}(x,t) \\partial_{j}u(x,t)) - \\frac{A}{|x|^{2+\\beta}} u(x,t)-\\partial_{t}u(x,t) =0\\quad (A>0,\\quad\\beta\\geq 0), \\end{equation} with critical or supercritical 0-order term coefficients which are beyond De Giorgi-Nash-Moser's Theory. We also prove, in some special cases, weak solutions are even differentiable. Previously P. Baras and J. A. Goldstein \\cite{Baras1984} treated the case when $A0$, $\\beta=0$ and $(a_{ij})=I$, P. D. Milman and Y. A. Semenov \\cite{Milman2003}\\cite{Milman2004} obtain bounds for the heat kernel.

  1. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model.

    Science.gov (United States)

    Wen, Zijuan; Fan, Meng; Asiri, Asim M; Alzahrani, Ebraheem O; El-Dessoky, Mohamed M; Kuang, Yang

    2017-04-01

    This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.

  2. The Calculation of Supersonic Flows with Strong Viscous-Inviscid Interaction Using the Parabolized Navier - Equations

    Science.gov (United States)

    Barnett, Mark

    This investigation is concerned with calculating strong viscous-inviscid interactions in two-dimensional laminar supersonic flows with and without separation. The equations solved are the so-called parabolized Navier-Stokes equations. The streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propogation of information. Global iteration is employed to repeatedly update the solution from an initial guess until convergence is achieved. Interacting boundary layer theory is discussed in order to provide some essential background information for the development of the present calculation technique. The numerical scheme used is an alternating direction explicit (ADE) procedure which is adapted from the Saul'yev method. This technique is chosen as an alternative to the more difficult to program multigrid strategy used by other investigators and the slower converging Gauss-Seidel method. Separated flows are computed using the ADE method. Only small or moderate separation bubbles are considered. This restriction permits simple approximations to the convective terms in reversed flow regions without introducing severe error since the reversed flow velocities are small. Results are presented for a number of geometries including compression ramps and humps on flat plates with separation. The present results are compared with those obtained by other investigators using the full Navier-Stokes equations and interacting boundary layer theory. Comparisons were found to be qualitatively good. The quantitative comparisons varied, however mesh refinement studies indicated that the parabolized Navier-Stokes solutions tended towards second-order accurate full Navier-Stokes solutions as well as interacting boundary layer solutions for which mesh refinement studies were also executed.

  3. Cauchy problem of semi-linear parabolic equations with weak data in homogeneous space and application to the Navier-Stokes equations

    Institute of Scientific and Technical Information of China (English)

    苗长兴

    2003-01-01

    In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations withweak data in the homogeneous spaces. We give a method which can be used to construct local mild solutionsof the abstract Cauchy problem in Cσ,s,p and Lq([O, T);Hs,p) by introducing the concept of both admissiblequintuplet and compatible space and establishing time-space estimates for solutions to the linear parabolic typeequations. For the small data, we prove that these results can be extended globally in time. We also study theregularity of the solution to the abstract Cauchy problem for nonlinear parabolic type equations in Cσ,s,p. Asan application, we obtain the same result for Navier-Stokes equations with weak initial data in homogeneousSobolev spaces.

  4. Self-similar singular solution of doubly singular parabolic equation with gradient absorption term

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term u t = div ( | ∇ u m | p − 2 ∇ u m − | ∇ u | q for 1$"> p > 1 , 1$"> m ( p − 1 > 1 and 1$"> q > 1 in ℝ n × ( 0 , ∞ . By shooting and phase plane methods, we prove that when {1+n}/({1+mn}q+{mn}/({mn+1}$"> p > 1 + n / ( 1 + m n q + m n / ( m n + 1 there exists self-similar singular solution, while p ≤ n + 1 / ( 1 + m n q + m n / ( m n + 1 there is no any self-similar singular solution. In case of existence, the self-similar singular solution is the self-similar very singular solutions which have compact support. Moreover, the interface relation is obtained.

  5. Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation

    KAUST Repository

    Jin, Bangti

    2014-01-01

    © 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

  6. An hp-local Discontinuous Galerkin Method for Parabolic Integro-Differential Equations

    KAUST Repository

    Pani, Amiya K.

    2010-06-06

    In this article, a priori error bounds are derived for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that error estimates in L 2-norm of the gradient as well as of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps us to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains. © 2010 Springer Science+Business Media, LLC.

  7. On study of the theory and algorithm of the three dimensional coupled mode-parabolic equation

    Institute of Scientific and Technical Information of China (English)

    PENG Zhaohui; ZHANG Renhe

    2004-01-01

    A fast algorithm of sound propagation in three dimensional underwater environments is presented. On the basis of the generalized phase integral (WKBZ) theory and the beam displacement ray mode (BDRM) theory, the coupled mode parabolic equation (CMPE)theory of sound propagation in range dependent underwater environment is extended for three dimensional (3D) problems. The CMPE3D solution is expressed in terms of the normal modes in vertical direction and the coupled mode amplitude coefficients in horizontal directions. By using the WKBZ theory and the BDRM theory, the local normal mode analysis can be processed efficiently. A pEobased algorithm, which was implemented in model FOR3D by Lee D et al ["Numerical Ocean Acoustic Propagation in Three Dimensions", World Scientific, Singapore,1995] is also adopted to solve the coupled mode amplitude coefficients. Numerical simulations indicate that the efficiency has been greatly improved by using CMPE3D instead of the PE approximations.

  8. Highly efficient H 1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

    Institute of Scientific and Technical Information of China (English)

    石东洋; 廖歆; 唐启立

    2014-01-01

    A highly effcient H 1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(Ω) norm and the flux p=∇u in H(div,Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

  9. Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data

    Science.gov (United States)

    Côte, Delphine; Côte, Raphaël

    2017-03-01

    We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).

  10. Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials

    Directory of Open Access Journals (Sweden)

    Xin Wang

    2014-01-01

    Full Text Available An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.

  11. Single-scattering parabolic equation solutions for elastic media propagation, including Rayleigh waves.

    Science.gov (United States)

    Metzler, Adam M; Siegmann, William L; Collins, Michael D

    2012-02-01

    The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.

  12. Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers

    Science.gov (United States)

    Kuehl, Joseph

    2016-11-01

    The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.

  13. On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient

    Directory of Open Access Journals (Sweden)

    John D. Towers

    2002-10-01

    Full Text Available We study the Cauchy problem for the nonlinear (possibly strongly degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(xf(u=partial_x^2 A(u, quad A'(cdotge 0, $$ where the coefficient $gamma(x$ is possibly discontinuous and $f(u$ is genuinely nonlinear, but not necessarily convex or concave. Existence of a weak solution is proved by passing to the limit as $varepsilondownarrow 0$ in a suitable sequence ${u_{varepsilon}}_{varepsilon>0}$ of smooth approximations solving the problem above with the transport flux $gamma(xf(cdot$ replaced by $gamma_{varepsilon}(xf(cdot$ and the diffusion function $A(cdot$ replaced by $A_{varepsilon}(cdot$, where $gamma_{varepsilon}(cdot$ is smooth and $A_{varepsilon}'(cdot>0$. The main technical challenge is to deal with the fact that the total variation $|u_{varepsilon}|_{BV}$ cannot be bounded uniformly in $varepsilon$, and hence one cannot derive directly strong convergence of ${u_{varepsilon}}_{varepsilon>0}$. In the purely hyperbolic case ($A'equiv 0$, where existence has already been established by a number of authors, all existence results to date have used a singular maolinebreak{}pping to overcome the lack of a variation bound. Here we derive instead strong convergence via a series of a priori (energy estimates that allow us to deduce convergence of the diffusion function and use the compensated compactness method to deal with the transport term. Submitted April 29, 2002. Published October 27, 2002. Math Subject Classifications: 35K65, 35D05, 35R05, 35L80 Key Words: Degenerate parabolic equation; nonconvex flux; weak solution; discontinuous coefficient; viscosity method; a priori estimates; compensated compactness

  14. Uniqueness of a very singular solution to nonlinear degenerate parabolic equations with absorption for Dirichlet boundary condition

    Directory of Open Access Journals (Sweden)

    Nguyen Anh Dao

    2016-11-01

    Full Text Available We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.

  15. Continuous Dependence on the Initial-time Geometry for a Parabolic Equation from Dynamo Theory with Different Prescribed Data

    Institute of Scientific and Technical Information of China (English)

    陈晨; 谭忠

    2005-01-01

    In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.

  16. A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

    Institute of Scientific and Technical Information of China (English)

    SHI Dong-yang; WANG Hui-min; LI Zhi-yan

    2009-01-01

    A lumped mass approximation scheme of a low order Crouzeix-Raviart type nonconforming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

  17. Domain Decomposition Method Modified by Characteristic Finite Element Procedure for System of Parabolic Equations with Discontinuous Coefficients

    Institute of Scientific and Technical Information of China (English)

    Luo Chang

    2006-01-01

    In this work, system of parabolic equations with discontinuous coefficients is studied. The domain decomposition method modified by a characteristic finite element procedure is applied. A function is defined to approximate the fluxes on inner boundaries by using the solution at the previous level. Thus the parallelism is achieved. Convergence analysis and error estimate are also presented.

  18. Eigenfunction approach to the Green's function parabolic equation in outdoor sound: A tutorial.

    Science.gov (United States)

    Gilbert, Kenneth E

    2016-03-01

    Understanding the physics and mathematics underlying a computational algorithm such as the Green's function parabolic equation (GFPE) is both useful and worthwhile. To this end, the present article aims to give a more widely accessible derivation of the GFPE algorithm than was given originally by Gilbert and Di [(1993). J. Acoust. Soc. Am. 94, 2343-2352]. The present derivation, which uses mathematics familiar to most engineers and physicists, begins with the separation of variables method, a basic and well-known approach for solving partial differential equations. The method leads naturally to eigenvalue-eigenfunction equations. A step-by-step analysis arrives at relatively simple, analytic expressions for the horizontal and vertical eigenfunctions, which are sinusoids plus a surface wave. The eigenfunctions are superposed in an eigenfunction expansion to yield a one-way propagation solution. The one-way solution is generalized to obtain the GFPE algorithm. In addition, and equally important, the eigenfunctions are used to give concrete meaning to abstract operator solutions for one-way acoustic propagation. By using an eigenfunction expansion of the acoustic field, together with an operator solution, one can obtain the GFPE algorithm very directly and concisely.

  19. 线性抛物Volterra差分方程的全局吸引性%Global Attractivity of Linear Parabolic Volterra Difference Equations

    Institute of Scientific and Technical Information of China (English)

    黄立

    2004-01-01

    In this paper, by constructing Liapunov Sequences, we study the golbal attractivity of linear Parabolic volterra difference equations of neutral type and obtain some sufficient conditions for the global attractivity of the zero solution of above equations.

  20. On a new nonlocal boundary value problem for an equation of the mixed parabolic-hyperbolic type

    Science.gov (United States)

    Dildabek, Gulnar

    2016-12-01

    In this work a new nonlocal boundary value problem for an equation of the mixed type is formulated. This equation is parabolic-hyperbolic and belongs to the first kind because the line of type change is not a characteristic of the equation. Non-local condition binds points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem is generalization of the well-known problems of Frankl type. A boundary value problem for the heat equation with conditions of the Samarskii-Ionlin type arises in solving this problem. Unlike the existing publications of the other authors related to the theme it is necessary to note that in this papers the nonlocal problems were considered in rectangular domains. But in our formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique strong solvability of the formulated problem is proved.

  1. Estimates of the rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations

    Science.gov (United States)

    Smagin, V. V.

    1997-04-01

    We consider a weakly solvable parabolic problem in a separable Hilbert space. We seek approximations to the exact solution by projective and projective-difference methods. In this connection the discretization of the problem with respect to the spatial variables is carried out by the semidiscrete method of Galerkin, and with respect to time by the implicit method of Euler. In this paper we establish a coercive mean-square error estimate for the approximate solutions. We illustrate the effectiveness of these estimates with parabolic equations of second order with Dirichlet or Neumann boundary conditions in projective subspaces of finite element type.

  2. Plane waves at or near grazing incidence in the parabolic approximation. [acoustic equations of motion for sound fields

    Science.gov (United States)

    Mcaninch, G. L.; Myers, M. K.

    1980-01-01

    The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.

  3. A Finite Volume Backward Euler Difference Method for Nonlinear Parabolic Integral-differential Equation%非线性抛物型积分-微分方程的向后Euler差分有限体积元方法

    Institute of Scientific and Technical Information of China (English)

    王波; 王强

    2009-01-01

    The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations.These results are new for finite volume element methods for parabolic integro-differential equations.

  4. A Numerical Solution for One-dimensional Parabolic Equation Using Pseudo-spectral Integration Matrix and FDM

    Directory of Open Access Journals (Sweden)

    Saeid Gholami

    2014-01-01

    Full Text Available This study presents a numerical method for the solution of one type of PDEs equation. In this study, apply the pseudo-spectral successive integration method to approximate the solution of the one-dimensional parabolic equation. This method is based on El-Gendi pseudo-spectral method. Also the Finite Difference Method (FDM is used as a minor method. The present numerical results are in satisfactory agreement with exact solution.

  5. The Extended Parabolic Equation Method and Implication of Results for Atmospheric Millimeter-Wave and Optical Propagation

    Science.gov (United States)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the -correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  6. A compactness lemma of Aubin type and its application to degenerate parabolic equations

    Directory of Open Access Journals (Sweden)

    Anvarbek Meirmanov

    2014-10-01

    Full Text Available Let $\\Omega\\subset \\mathbb{R}^{n}$ be a regular domain and $\\Phi(s\\in C_{\\rm loc}(\\mathbb{R}$ be a given function. If $\\mathfrak{M}\\subset L_2(0,T;W^1_2(\\Omega \\cap L_{\\infty}(\\Omega\\times (0,T$ is bounded and the set $\\{\\partial_t\\Phi(v|\\,v\\in \\mathfrak{M}\\}$ is bounded in $L_2(0,T;W^{-1}_2(\\Omega$, then there is a sequence $\\{v_k\\}\\in \\mathfrak{M}$ such that $v_k\\rightharpoonup v \\in L^2(0,T;W^1_2(\\Omega$, and $v_k\\to v$, $\\Phi(v_k\\to \\Phi(v$ a.e. in $\\Omega_T=\\Omega\\times (0,T$. This assertion is applied to prove solvability of the one-dimensional initial and boundary-value problem for a degenerate parabolic equation arising in the Buckley-Leverett model of two-phase filtration. We prove existence and uniqueness of a weak solution, establish the property of finite speed of propagation and construct a self-similar solution.

  7. Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

    Energy Technology Data Exchange (ETDEWEB)

    Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)

    2015-08-15

    Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.

  8. Leading-order cross term correction of three-dimensional parabolic equation models.

    Science.gov (United States)

    Sturm, Frédéric

    2016-01-01

    The issue of handling a leading-order cross-multiplied term in three-dimensional (3D) parabolic equation (PE) based models is addressed. In particular, numerical results obtained incorporating a leading-order cross-term correction in an existing 3D PE model, written in cylindrical coordinates, based on higher-order Padé approximations in both depth and azimuth, and a splitting operator technique are reported. Note that the numerical algorithm proposed in this paper could be used in the future to update any 3D PE codes that neglect cross terms and use a splitting numerical technique. The 3D penetrable wedge benchmark problem is chosen to illustrate the accuracy of the now-fully wide-angle enhanced 3D PE model. The comparisons with a 3D reference solution based on the image source clearly show that handling the leading-order cross term in the 3D PE computation is sufficient to remove the phase errors inherent to any 3D PE models that neglect cross terms in their formulations.

  9. Prediction of far-field wind turbine noise propagation with parabolic equation.

    Science.gov (United States)

    Lee, Seongkyu; Lee, Dongjai; Honhoff, Saskia

    2016-08-01

    Sound propagation of wind farms is typically simulated by the use of engineering tools that are neglecting some atmospheric conditions and terrain effects. Wind and temperature profiles, however, can affect the propagation of sound and thus the perceived sound in the far field. A better understanding and application of those effects would allow a more optimized farm operation towards meeting noise regulations and optimizing energy yield. This paper presents the parabolic equation (PE) model development for accurate wind turbine noise propagation. The model is validated against analytic solutions for a uniform sound speed profile, benchmark problems for nonuniform sound speed profiles, and field sound test data for real environmental acoustics. It is shown that PE provides good agreement with the measured data, except upwind propagation cases in which turbulence scattering is important. Finally, the PE model uses computational fluid dynamics results as input to accurately predict sound propagation for complex flows such as wake flows. It is demonstrated that wake flows significantly modify the sound propagation characteristics.

  10. Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

    KAUST Repository

    Nobile, Fabio

    2009-11-05

    We consider the problem of numerically approximating statistical moments of the solution of a time- dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochastic coefficients of the PDE are approximated by truncated Karhunen-Loève expansions driven by a finite number of uncorrelated random variables. After approxi- mating the stochastic coefficients, the original stochastic PDE turns into a new deterministic parametric PDE of the same type, the dimension of the parameter set being equal to the number of random variables introduced. After proving that the solution of the parametric PDE problem is analytic with respect to the parameters, we consider global polynomial approximations based on tensor product, total degree or sparse polynomial spaces and constructed by either a Stochastic Galerkin or a Stochastic Collocation approach. We derive convergence rates for the different cases and present numerical results that show how these approaches are a valid alternative to the more traditional Monte Carlo Method for this class of problems. © 2009 John Wiley & Sons, Ltd.

  11. A proof of the parabolic Schauder estimates using Trudinger's method and the mean value property of the heat equation

    CERN Document Server

    Baker, Charles

    2012-01-01

    One method available to prove the Schauder estimates is Neil Trudinger's method of mollification. In the case of second order elliptic equations, the method requires little more than mollification and the solid mean value inequality for subharmonic functions. Our goal in this article is show how the mean value property of subsolutions of the heat equation can be used in a similar fashion as the solid mean value inequality for subharmonic functions in Trudinger's original elliptic treatment, providing a relatively simple derivation of the interior Schauder estimate for second order parabolic equations.

  12. Degenerate-parabolic partial differential equations with unbounded coefficients, martingale problems, and a mimicking theorem for Ito processes

    CERN Document Server

    Feehan, Paul M N

    2011-01-01

    We solve four intertwined problems, motivated by mathematical finance, concerning degenerate-parabolic partial differential operators and degenerate diffusion processes. First, we consider a parabolic partial differential equation on a half-space whose coefficients are suitably Holder continuous and allowed to grow linearly in the spatial variable and which becomes degenerate along the boundary of the half-space. We establish existence and uniqueness of solutions in weighted Holder spaces which incorporate both the degeneracy at the boundary and the unboundedness of the coefficients. Second, we show that the martingale problem associated with a degenerate elliptic differential operator with unbounded, locally Holder continuous coefficients on a half-space is well-posed in the sense of Stroock and Varadhan. Third, we prove existence, uniqueness, and the strong Markov property for weak solutions to a stochastic differential equation with degenerate diffusion and unbounded coefficients with suitable H\\"older con...

  13. L{sup p} Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

    Energy Technology Data Exchange (ETDEWEB)

    Du Kai, E-mail: kdu@fudan.edu.cn; Qiu, Jinniao, E-mail: 071018032@fudan.edu.cn; Tang Shanjian, E-mail: sjtang@fudan.edu.cn [Fudan University, Department of Finance and Control Sciences, School of Mathematical Sciences, and Laboratory of Mathematics for Nonlinear Sciences (China)

    2012-04-15

    This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L{sup p}-theory is given for the Cauchy problem of BSPDEs, separately for the case of p Element-Of (1,2] and for the case of p Element-Of (2,{infinity}). A comparison theorem is also addressed.

  14. Solution of Two-dimensional Parabolic Equation Subject to Non-local Boundary Conditions Using Homotopy Perturbation Method

    Directory of Open Access Journals (Sweden)

    Puskar Raj SHARMA

    2012-01-01

    Full Text Available Aim of the paper is to investigate solution of twodimensional linear parabolic partial differential equation with non-local boundary conditions using Homotopy Perturbation Method (HPM. This method is not only reliable in obtaining solution of such problems in series form with high accuracy but it also guarantees considerable saving of the calculation volume and time as compared to other methods. The application of the method has been illustrated through an example

  15. LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LiFengquan

    2002-01-01

    In this paper,we discuss the limit behaviour of solutions to equivalued surface boundayr value problem for parabolic equatiopns when the equivalued surface boundary shriks to a point and the space dimension of the domain is two or more.

  16. THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

    Institute of Scientific and Technical Information of China (English)

    WEN Guochun; HUANG Sha; QIAO Yuying

    2001-01-01

    In 1988, Yu. A. Alkhutov and I. T. Mamedov discussed the solvability of the Dirichlet problem for linear uniformly parabolic equations with measurable coefficients where the coefficients satisfy the condition In this paper, we try to generalize the results of Alkhutov and Mamedov to nonlinear uni-formly parabolic systems of second order equations with measurable coefficients; moreover,we also discuss the solvability of the Neumann problem for the above systems.

  17. Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions

    Science.gov (United States)

    Mittal, R. C.; Jain, R. K.

    2012-12-01

    In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.

  18. Existence of Renormalized Solutions for p(x-Parabolic Equation with three unbounded nonlinearities

    Directory of Open Access Journals (Sweden)

    Youssef Akdim

    2016-04-01

    Full Text Available In this article, we study the existence of renormalized solution for the nonlinear $p(x$-parabolic problem of the form:\\\\ $\\begin{cases} \\frac{\\partial b(x,u}{\\partial t} - div (a(x,t,u,\

  19. Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation

    Institute of Scientific and Technical Information of China (English)

    赵俊宁; 徐中海

    1996-01-01

    The Cauchy problem and initial traces for the doubly degenerate parabolic equationsare studied. Under certain growth condition on the initial datum u0(x) as the existence of solution is proved. The results obtained are optimal in the dass of nonnegative locally bounded solution, for which a Harnack-type inequality holds.

  20. Computationally efficient parabolic equation solutions to seismo-acoustic problems involving thin or low-shear elastic layers.

    Science.gov (United States)

    Metzler, Adam M; Collis, Jon M

    2013-04-01

    Shallow-water environments typically include sediments containing thin or low-shear layers. Numerical treatments of these types of layers require finer depth grid spacing than is needed elsewhere in the domain. Thin layers require finer grids to fully sample effects due to elasticity within the layer. As shear wave speeds approach zero, the governing system becomes singular and fine-grid spacing becomes necessary to obtain converged solutions. In this paper, a seismo-acoustic parabolic equation solution is derived utilizing modified difference formulas using Galerkin's method to allow for variable-grid spacing in depth. Propagation results are shown for environments containing thin layers and low-shear layers.

  1. On the uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations

    Energy Technology Data Exchange (ETDEWEB)

    Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H.

    2002-04-01

    We prove uniqueness and existence of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. The uniqueness proof is an adaption of Kruzkov's ''doubling of variables'' proof. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. We also present a numerical example motivated by biodegradation in porous media.

  2. Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in Lp

    Directory of Open Access Journals (Sweden)

    Sandjo Albert N.

    2014-01-01

    Full Text Available We establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C0([0, T]; Lp(Ω by introducing appropriate time-weighted Lebesgue norms inspired by a priori estimates of solutions. This framework allows us to obtain global existence of solutions under the proviso that initial data are reasonably small

  3. EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L1 DATA

    Institute of Scientific and Technical Information of China (English)

    Kaouther AMMAR; Hicham REDWANE

    2014-01-01

    We study a class of nonlinear parabolic equations of the type:∂b(u)∂t -diva(x, t, u)∇u+g(u)|∇u|2=f, where the right hand side belongs to L1(Q), b is a strictly increasing C1-function and-div(a(x, t, u)∇u) is a Leray-Lions operator. The function g is just assumed to be con-tinuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.

  4. Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

    Science.gov (United States)

    Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

    2016-05-01

    Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

  5. A stabilized Runge–Kutta–Legendre method for explicit super-time-stepping of parabolic and mixed equations

    Energy Technology Data Exchange (ETDEWEB)

    Meyer, Chad D.; Balsara, Dinshaw S. [Physics Department, Univ. of Notre Dame, 225 Nieuwland Science Hall, Notre Dame, IN 46556 (United States); Aslam, Tariq D. [WX-9 Group, Los Alamos National Laboratory, MS P952, Los Alamos, NM 87545 (United States)

    2014-01-15

    Parabolic partial differential equations appear in several physical problems, including problems that have a dominant hyperbolic part coupled to a sub-dominant parabolic component. Explicit methods for their solution are easy to implement but have very restrictive time step constraints. Implicit solution methods can be unconditionally stable but have the disadvantage of being computationally costly or difficult to implement. Super-time-stepping methods for treating parabolic terms in mixed type partial differential equations occupy an intermediate position. In such methods each superstep takes “s” explicit Runge–Kutta-like time-steps to advance the parabolic terms by a time-step that is s{sup 2} times larger than a single explicit time-step. The expanded stability is usually obtained by mapping the short recursion relation of the explicit Runge–Kutta scheme to the recursion relation of some well-known, stable polynomial. Prior work has built temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Chebyshev polynomials. Since their stability is based on the boundedness of the Chebyshev polynomials, these methods have been called RKC1 and RKC2. In this work we build temporally first- and second-order accurate super-time-stepping methods around the recursion relation associated with Legendre polynomials. We call these methods RKL1 and RKL2. The RKL1 method is first-order accurate in time; the RKL2 method is second-order accurate in time. We verify that the newly-designed RKL1 and RKL2 schemes have a very desirable monotonicity preserving property for one-dimensional problems – a solution that is monotone at the beginning of a time step retains that property at the end of that time step. It is shown that RKL1 and RKL2 methods are stable for all values of the diffusion coefficient up to the maximum value. We call this a convex monotonicity preserving property and show by examples that it is very

  6. Explicit and implicit ode solvers using Krylov subspace optimization: Application to the diffusion equation and parabolic Maxwell`s system

    Energy Technology Data Exchange (ETDEWEB)

    Druskin, V.; Knizhnerman, L.

    1994-12-31

    The authors solve the Cauchy problem for an ODE system Au + {partial_derivative}u/{partial_derivative}t = 0, u{vert_bar}{sub t=0} = {var_phi}, where A is a square real nonnegative definite symmetric matrix of the order N, {var_phi} is a vector from R{sup N}. The stiffness matrix A is obtained due to semi-discretization of a parabolic equation or system with time-independent coefficients. The authors are particularly interested in large stiff 3-D problems for the scalar diffusion and vectorial Maxwell`s equations. First they consider an explicit method in which the solution on a whole time interval is projected on a Krylov subspace originated by A. Then they suggest another Krylov subspace with better approximating properties using powers of an implicit transition operator. These Krylov subspace methods generate optimal in a spectral sense polynomial approximations for the solution of the ODE, similar to CG for SLE.

  7. Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

    Science.gov (United States)

    Dong, Hao; Nie, Yu-Feng; Cui, Jun-Zhi; Wu, Ya-Tao

    2015-09-01

    We study the hyperbolic-parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed. Project supported by the National Natural Science Foundation of China (Grant No. 11471262), the National Basic Research Program of China (Grant No. 2012CB025904), and the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University, China.

  8. Numerical Simulation of Wave-Induced Currents Combined with Parabolic Mild-Slope Equation in Curvilinear Coordinates

    Institute of Scientific and Technical Information of China (English)

    CUI Lei; TONG Fei-fei; SHI Feng

    2011-01-01

    Researches on breaking-induced currents by waves are summarized firstly in this paper.Then,a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline.The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation.The wave module actually serves as the driving force to provide the current module with required radiation stresses.The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module,respectively.The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater.The numerical results are compared with the measured data and published numerical results.

  9. A three-dimensional parabolic equation model of sound propagation using higher-order operator splitting and Padé approximants.

    Science.gov (United States)

    Lin, Ying-Tsong; Collis, Jon M; Duda, Timothy F

    2012-11-01

    An alternating direction implicit (ADI) three-dimensional fluid parabolic equation solution method with enhanced accuracy is presented. The method uses a square-root Helmholtz operator splitting algorithm that retains cross-multiplied operator terms that have been previously neglected. With these higher-order cross terms, the valid angular range of the parabolic equation solution is improved. The method is tested for accuracy against an image solution in an idealized wedge problem. Computational efficiency improvements resulting from the ADI discretization are also discussed.

  10. Optimal Error Estimates of Two Mixed Finite Element Methods for Parabolic Integro-Differential Equations with Nonsmooth Initial Data

    KAUST Repository

    Goswami, Deepjyoti

    2013-05-01

    In the first part of this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to the standard mixed method for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments combined with a repeated use of an integral operator and without using parabolic type duality technique, optimal L2 L2-error estimates are derived for semidiscrete approximations, when the initial condition is in L2 L2. Due to the presence of the integral term, it is, further, observed that a negative norm estimate plays a crucial role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof techniques used in deriving optimal error estimates for finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, we extend the proposed analysis to the standard mixed method for PIDE with rough initial data and provide an optimal error estimate in L2, L 2, which improves upon the results available in the literature. © 2013 Springer Science+Business Media New York.

  11. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2014-01-01

    Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  12. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

    Science.gov (United States)

    Motsa, S S; Magagula, V M; Sibanda, P

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  13. Stochastic integration in Banach spaces and applications to parabolic evolution equations

    NARCIS (Netherlands)

    Veraar, M.C.

    2006-01-01

    Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness re

  14. Stochastic integration in Banach spaces and applications to parabolic evolution equations

    NARCIS (Netherlands)

    Veraar, M.C.

    2006-01-01

    Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness

  15. Experimental studies on illposed singularly perturbed boundary value problems for parabolic differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Reinhardt, Hans-Juergen, E-mail: reinhardt@mathematik.uni-siegen.de [Department of Mathematics, University of Siegen, Emmy-Noether-Campus, Walter-Flex-Str. 3, D-57072 Siegen (Germany)

    2011-04-01

    In this paper singularly perturbed parabolic initial-boundary value problems are considered which, in addition, are illposed. The latter means that at one end of the 1-d spatial domain two conditions (for the solution and its spatial derivative) are given while on the other end the corresponding quantities are to be determined. It is well-known that such problems are illposed in the mathematical sense. Here, in addition, boundary layers may occur which make the problems more difficult. For relatively simple examples numerical experiments have been carried out and numerical results are shown. The Conjugate Gradient Methods is used to find the desired quantities iteratively. It will be explained what has to be done in any iteration step. A regularisation is performed by means of discretization and by determining an optimal final iteration step via a stopping rule.

  16. Corrected explicit-implicit domain decomposition algorithms for two-dimensional semilinear parabolic equations

    Institute of Scientific and Technical Information of China (English)

    LIAO HongLin; SHI HanSheng; SUN ZhiZhong

    2009-01-01

    Corrected explicit-implicit domain decomposition (CEIDD) algorithms are studied for parallel approximation of semilinear parabolic problems on distributed memory processors. It is natural to divide the spatial domain into some smaller parallel strips and cells using the simplest straight-line interface (SI). By using the Leray-Schauder fixed-point theorem and the discrete energy method, it is shown that the resulting CEIDD-SI algorithm is uniquely solvable, unconditionally stable and convergent. The CEIDD-SI method always suffers from the globalization of data communication when interior boundaries cross into each other inside the domain. To overcome this disadvantage, a composite interface (CI) that consists of straight segments and zigzag fractions is suggested. The corresponding CEIDD-CI algorithm is proven to be solvable, stable and convergent. Numerical experiments are presented to support the theoretical results.

  17. FINITE VOLUME NUMERICAL ANALYSIS FOR PARABOLIC EQUATION WITH ROBIN BOUNDARY CONDITION

    Institute of Scientific and Technical Information of China (English)

    Xia Cui

    2005-01-01

    In this paper, finite volume method on unstructured meshes is studied for a parabolic convection-diffusion problem on an open bounded set of Rd (d = 2 or 3) with Robin boundary condition. Upwinding approximations are adapted to treat both the convection term and Robin boundary condition. By directly getting start from the formulation of the finite volume scheme, numerical analysis is done. By using several discrete functional analysis techniques such as summation by parts, discrete norm inequality, et al, the stability and error estimates on the approximate solution are established, existence and uniqueness of the approximate solution and the 1st order temporal norm and L2 and H1 spacial norm convergence properties are obtained.

  18. 一类抛物方程的广义解%Generalized Solutions of a Class of Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    李悦

    2014-01-01

    This paper discusses the solution about a class of Parabolic Equations with non-homogeneous boundary value problem,using the method of variable substitution to transform the non-homogeneous boundary value problem into a homogeneous boundary value problem,and using the Rothe methods to prove the existence and uniqueness of the solution.%文中讨论了一类抛物方程非齐次边值问题的解法,利用变量替换法将非齐次边值问题转化为齐次边值问题,运用Rothe方法证明了其解的存在唯一性。

  19. EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

    Institute of Scientific and Technical Information of China (English)

    Han Junqiang; Wang Yongda; Niu Pengcheng

    2012-01-01

    We study the existence of solutions to the following parabolic equation {ut-△pu =λ/|x|s|u|q-2 u,(x,t) ∈ Ω × (0,∞),u(x,0) =f(x),x ∈ Ω,(P)u(x,t) =0,(x,t) ∈ δΩ × (0,∞),where-△pu ≡-div(|▽u|p-2 ▽u),1 < p < N,0 < s ≤ p,p≤s≤ q ≤ p*(s) =N-s/N-pp,Ω is a bounded domain in RN such that 0 ∈ Ω with a C1 boundary δΩ,f ≥ 0 satisfying some convenient regularity assumptions.The analysis reveals that the existence of solutions for (P) depends on p,q,s in general,and on the relation between λ and the best constant in the Sobolev-Hardy inequality.

  20. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

    Science.gov (United States)

    A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

  1. 一个奇异抛物方程Neumann问题的可解性%The Solvability of Neumann Problem for a Singular Parabolic Equation

    Institute of Scientific and Technical Information of China (English)

    李刚

    2008-01-01

    The qualitative properties of solutions of a Neumann problem for the singular parabolic equation ut=(um-1ux)x(-1<m≤0)is studied in this paper.It is proved that there exists a unique global smooth solution which depends on the initial value.The large time behavior of the solutions is also discussed.

  2. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

    Science.gov (United States)

    A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

  3. Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

    Science.gov (United States)

    Krylov, N. V.; Priola, E.

    2017-09-01

    We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

  4. Continuity of Some Classes of Functions Related to Degenerate Parabolic Equations and Its Applications%源于退化抛物方程某些函数类的连续性研究及其应用

    Institute of Scientific and Technical Information of China (English)

    宋斌恒; 袁聪

    2002-01-01

    We study some classes of functions satisfying the assumptions similar tobut weaker than those for the classical B2 function classes used in the research ofquasi-linear parabolic equations as well as the ones used in the research of degenerateparabolic equations including porous medium equations. Consequently, we prove thata function in such a class is continuous. As an application, we obtain the estimatefor the continuous modulus of the solutions of a few degenerate parabolic equationsin divergence form, including the anisotropic porous equations.

  5. On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification

    Directory of Open Access Journals (Sweden)

    Abdelfatah Bouziani

    2003-01-01

    Full Text Available This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem.

  6. On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f|||h and h, we give the suffcient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.

  7. On the existence of Lipschitz solutions to some forward-backward parabolic equations

    Science.gov (United States)

    Kim, Seonghak

    In this dissertation we discuss a new approach for studying forward-backward quasilinear diffusion equations. Our main idea is motivated by a reformulation of such equations as non-homogeneous partial differential inclusions and relies on a Baire's category method. In this way the existence of Lipschitz solutions to the initial-boundary value problem of those equations is guaranteed under a certain density condition. Finally we study two important cases of anisotropic diffusion in which such density condition can be realized. The first case is on the Perona-Malik type equations. In 1990, P. Perona and J. Malik [35] proposed an anisotropic diffusion model, called the Perona-Malik model, in image processing ut = div (| Du|/ 1 + Du 2) for denoising and edge enhancement of a computer vision. Since then the dichotomy of numerical stability and theoretical ill-posedness of the model has attracted many interests in the name of the Perona-Malik paradox [28]. Our result in this case provides the model with mathematically rigorous solutions in any dimension that are even reflecting some phenomena observed in numerical simulations. The other case deals with the existence result on the Hollig type equations. In 1983, K. Hollig [20] proved, in dimension n = 1, the existence of infinitely many L2-weak solutions to the initial-boundary value problem of a forward-backward diffusion equation with non-monotone piecewise linear heat flux, and this piecewise linearity was much relaxed later by K. Zhang [45]. The work [20] was initially motivated by the Clausius-Duhem inequality in the second law of thermodynamics, where the negative of the heat flux may violate the monotonicity but should obey the Fourier inequality at least. Our result in this case generalizes [20, 45] to all dimensions.

  8. An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

    Science.gov (United States)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  9. Certain theorems on two dimensional Laplace transform and non-homogeneous parabolic partial differential equations

    Directory of Open Access Journals (Sweden)

    A. Aghili

    2011-12-01

    Full Text Available In this work,we present new theorems on two-dimensional Laplace transformation. We also develop some applications based on these results. The two-dimensional Laplace transformation is useful in the solution of non-homogeneous partial differential equations. In the last section a boundary value problem is solved by using the double Laplace-Carson transform.

  10. Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure

    Institute of Scientific and Technical Information of China (English)

    Hui Jun FAN

    2004-01-01

    This paper discusses the Cauchy problem of the equation ut=△·(|△um|p-2△um)-uq with initial datum a measure. Under the assumption of the parameters, one proves the existence and non-existence of the non-negative generalized solution.

  11. An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

    Science.gov (United States)

    Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

    2017-10-01

    In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

  12. The entropy solution of a hyperbolic-parabolic mixed type equation.

    Science.gov (United States)

    Zhan, Huashui

    2016-01-01

    The entropy solution of the equation [Formula: see text]is considered. Besides the usual initial value, only a partial boundary value is imposed. By choosing some special test functions, the stability of the solutions is obtained by Kruzkov's bi-variables method, provided that [Formula: see text] is an unit n-dimensional cube or the half space.

  13. H\\"older Estimates for Singular Non-local Parabolic Equations

    CERN Document Server

    Kim, Sunghoon

    2011-01-01

    In this paper, we establish local H\\"older estimate for non-negative solutions of the singular equation \\eqref{eq-nlocal-PME-1} below, for $m$ in the range of exponents $(\\frac{n-2\\sigma}{n+2\\sigma},1)$. Since we have trouble in finding the local energy inequality of $v$ directly. we use the fact that the operator $(-\\La)^{\\sigma}$ can be thought as the normal derivative of some extension $v^{\\ast}$ of $v$ to the upper half space, \\cite{CS}, i.e., $v$ is regarded as boundary value of $v^{\\ast}$ the solution of some local extension problem. Therefore, the local H\\"older estimate of $v$ can be obtained by the same regularity of $v^{\\ast}$. In addition, it enables us to describe the behaviour of solution of non-local fast diffusion equation near their extinction time.

  14. A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation

    Institute of Scientific and Technical Information of China (English)

    Grigory I. Shishkin

    2008-01-01

    A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence. The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find a priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in x, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im-proving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical so-lution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N-1 = o(ev), where N denotes the number of nodes in the spatial mesh, and the value v=v(K) can be chosen arbitrarily small for suitable K.

  15. Treatment of a sloping fluid-solid interface and sediment layering with the seismo-acoustic parabolic equation.

    Science.gov (United States)

    Collins, Michael D; Siegmann, William L

    2015-01-01

    The parabolic equation method is extended to handle problems in seismo-acoustics that have multiple fluid and solid layers, continuous depth dependence within layers, and sloping interfaces between layers. The medium is approximated in terms of a series of range-independent regions, and a single-scattering approximation is used to compute transmitted fields across the vertical interfaces between regions. The approach is implemented in terms of a set of dependent variables that is well suited to piecewise continuous depth dependence in the elastic parameters, but one of the fluid-solid interface conditions in that formulation involves a second derivative that complicates the treatment of sloping interfaces. This issue is resolved by using a non-centered, four-point difference formula for the second derivative. The approach is implemented using a matrix decomposition that is efficient when the parameters of the medium have a general dependence within the upper layers of the sediment but only depend on depth in the water column and deep within the sediment.

  16. The inverse problem of recovering the source in a parabolic equation under a condition of nonlocal observation

    Energy Technology Data Exchange (ETDEWEB)

    Kostin, A B [National Research Nuclear University ' Moscow Engineering Physics Institute' , Moscow (Russian Federation)

    2013-10-31

    We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.

  17. Massively parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations

    CERN Document Server

    Dyja, Robert; van der Zee, Kristoffer G

    2016-01-01

    We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...

  18. Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations

    KAUST Repository

    Jin, Bangti

    2013-01-01

    We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.

  19. Numerical study of a parametric parabolic equation and a related inverse boundary value problem

    Science.gov (United States)

    Mustonen, Lauri

    2016-10-01

    We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the nonhomogeneous diffusion coefficient in the interior of an object. The method in this paper relies on solving the forward problem for a whole family of diffusivities by using a spectral Galerkin method in the high-dimensional parameter domain. The evaluation of the parametric solution and its derivatives is then completely independent of spatial and temporal discretizations. In the case of a quadratic approximation for the parameter dependence and a direct solver for linear least squares problems, we show that the evaluation of the parametric solution does not increase the complexity of any linearized subproblem arising from a Gauss-Newtonian method that is used to minimize a Tikhonov functional. The feasibility of the proposed algorithm is demonstrated by diffusivity reconstructions in two and three spatial dimensions.

  20. On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of pressure filtration

    Energy Technology Data Exchange (ETDEWEB)

    Buerger, R.; Frid, H.; Karlsen, K.H.

    2002-07-01

    We consider a free boundary problem of a quasilinear strongly degenerate parabolic equation arising from a model of pressure filtration of flocculated suspensions. We provide definitions of generalized solutions of the free boundary problem in the framework of L2 divergence-measure fields. The formulation of boundary conditions is based on a Gauss-Green theorem for divergence-measure fields on bounded domains with Lipschitz deformable boundaries and avoids referring to traces of the solution. This allows to consider generalized solutions from a larger class than BV. Thus it is not necessary to derive the usual uniform estimates on spatial and time derivatives of the solutions of the corresponding regularized problem requires in the BV approach. We first prove existence and uniqueness of the solution of the regularized parabolic free boundary problem and then apply the vanishing viscosity method to prove existence of a generalized solution to the degenerate free boundary problem. (author)

  1. OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES

    Institute of Scientific and Technical Information of China (English)

    汪更生

    2001-01-01

    This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations.The maximum principle and some kind of approximate controllability are studied.

  2. High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

    Science.gov (United States)

    Manning, Robert M.

    2012-01-01

    The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

  3. On the numerical solution of parabolic equations in a single space variable by the continuous time galerkin method

    NARCIS (Netherlands)

    Bakker, M.

    1980-01-01

    We consider the Galerkin method to solve a parabolic initial boundary value problem in one space variable, using piecewise polynomial functions and give an alternative proof of superconvergence. Then by means of Lobatto quadrature, we obtain purely explicit vector initial value problems without loss

  4. Analyticity of Essentially Bounded Solutions to Semilinear Parabolic Systems and Validity of the Ginzburg-Landau Equation

    NARCIS (Netherlands)

    A. Doelman; P. Takác; P. Bollerman; A. van Harten; E.S. Titi

    1996-01-01

    Some analytic smoothing properties of a general strongly coupled, strongly parabolic semilinear system of order $2m$ in $realnos^D times (0,T)$ with analytic entries are investigated. These properties are expressed in terms of holomorphic continuation in space and time of essentially bounded global

  5. A Finite Difference Method for Solving Parabolic Equation%一类抛物型方程的有限差分法

    Institute of Scientific and Technical Information of China (English)

    刘相国; 徐富强

    2011-01-01

    This paper uses finite difference method to solve the boundary value problem of parabolic equation, obtaining the corresponding stability analysis and numerical simulation. Simulation results show that the method is feasible and effective.%利用有限差分法求解了抛物型方程边值问题,得到了相应的稳定性分析,并进行了数值模拟。模拟结果表明该方法是可行的、有效的。

  6. Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

    Directory of Open Access Journals (Sweden)

    Yuan Wang

    2015-01-01

    Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

  7. Nonlinear parabolic equations with blowing-up coefficients with respect to the unknown and with soft measure data

    Directory of Open Access Journals (Sweden)

    Khaled Zaki

    2016-12-01

    Full Text Available We establish the existence of solutions for the nonlinear parabolic problem with Dirichlet homogeneous boundary conditions, $$ \\frac{\\partial u}{\\partial t} - \\sum_{i=1}^N\\frac{\\partial}{\\partial x_i} \\Big( d_i(u\\frac{\\partial u}{\\partial x_i} \\Big =\\mu,\\quad u(t=0=u_0, $$ in a bounded domain. The coefficients $d_i(s$ are continuous on an interval $]-\\infty,m[$, there exists an index p such that $d_p(u$ blows up at a finite value m of the unknown u, and $\\mu$ is a diffuse measure.

  8. Local Petrovskii lacunas close to parabolic singular points of the wavefronts of strictly hyperbolic partial differential equations

    Science.gov (United States)

    Vassiliev, V. A.

    2016-10-01

    We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions of strictly hyperbolic PDEs with constant coefficients in {R}^N) close to parabolic singular points of their wavefronts (that is, at the points of types P_8^1, P_8^2, +/- X_9, X_9^1, X_9^2, J10^1 and J10^3). These points form the next most difficult family of classes in the natural classification of singular points after the so-called simple singularities A_k, D_k, E_6, E_7 and E_8, which have been investigated previously. Also we present a computer program which counts the topologically distinct morsifications of critical points of smooth functions, and hence also the local components of the complement of a generic wavefront at its singular points. Bibliography: 22 titles.

  9. GLOBAL ASYMPTOTICS TOWARD THE RAREFACTION WAVES FOR A PARABOLIC-ELLIPTIC SYSTEM RELATED TO THE CAMASSA-HOLM SHALLOW WATER EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ma Xuan; Yin Hui; Jing Jin

    2009-01-01

    This article is concerned with the global existence and large time behavior of solutions to the Cauchy problem for a parabolic-elliptic system related to the Camassa-Holm shallow water equation with the initial data u(0,x) = u0(x)→±, as x→±∞. (Ⅰ) Here, u- 0 for all u under consideration. Main aim of this article is to study the relation between solutions to the above Cauchy problem and those to the Riemann problem of the following nonlinear conservation law It is well known that if u- (x) - U(0,x) ∈H1(R) and u- < u+, the above Cauchy problem (E) and (I) admits a unique global classical solution u(t, x) which tends to the rarefaction wave uR(x/t) as t→+∞ in the maximum norm. The proof is given by an elementary energy method.

  10. 非线性抛物型方程有限元法数值积分的有效性%THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    哲曼

    2001-01-01

    The effect of numerical integration in finite element methods applied to a class of nonlinear parabolic equations is considered and some sufficient conditions on the quadrature scheme to ensure that the order of convergence is unaltered in the presence of numerical integration are given. Optimal L2 and H1 estimates for the error and its time derivative are established.

  11. LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF IMPLICIT DIFFERENCE SCHEME FOR A SEMI-LINEAR PARABOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    Zhi-zhong Sun; Long-Jun Shen

    2003-01-01

    In this paper, the solution of back-Euler implicit difference scheme for a semi-linearparabolic equation is proved to converge to the solution of difference scheme for the corre-sponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behaviorof its discrete solution is obtained which is analogous to that of its continuous solution. Atlast, a few results are also presented for Crank-Nicolson scheme.

  12. A numerical study of mixed parabolic-gradient systems

    NARCIS (Netherlands)

    Verwer, J.G.; Sommeijer, B.P.

    2000-01-01

    This paper is concerned with the numerical solution of parabolic equations coupled to gradient equations. The gradient equations are ordinary differential equations whose solutions define positions of particles in the spatial domain of the parabolic equations. The vector field of the gradient equati

  13. Superconvergence of Finite Element Approximations to Parabolic and Hyperbolic Integro-Differential Equations%抛物型和双曲型积分-微分方程有限元逼近的超收敛性质

    Institute of Scientific and Technical Information of China (English)

    张铁; 李长军

    2001-01-01

    The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables.

  14. New Criteria for Oscillation of Vector Parabolic Equations with Continuous Distribution Arguments%具连续分布变元的向量抛物型方程振动性的新准则

    Institute of Scientific and Technical Information of China (English)

    李元旦; 罗李平; 俞元洪

    2011-01-01

    The oscillations of a class of vector parabolic partial differential equations with continuous distribution arguments are studied. By employing the concept of H-oscillation and the method of reducing dimension with inner product, the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional differential inequalities have not eventually positive solution. Some new sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Dirichlet boundary condition,where H is a unit vector of RM.

  15. Well-posedness of nonlocal parabolic differential problems with dependent operators.

    Science.gov (United States)

    Ashyralyev, Allaberen; Hanalyev, Asker

    2014-01-01

    The nonlocal boundary value problem for the parabolic differential equation v'(t) + A(t)v(t) = f(t) (0 ≤ t ≤ T), v(0) = v(λ) + φ, 0 parabolic equations with dependent coefficients are established.

  16. Parabolic-like maps

    CERN Document Server

    Lomonaco, Luciana Luna Anna

    2011-01-01

    In this paper we introduce the notion of parabolic-like mapping, which is an object similar to a polynomial-like mapping, but with a parabolic external class, i.e. an external map with a parabolic fixed point. We prove a straightening theorem for parabolic-like maps, which states that any parabolic-like map of degree 2 is hybrid conjugate to a member of the family Per_1(1), and this member is unique (up to holomorphic conjugacy) if the filled Julia set of the parabolic-like map is connected.

  17. Stochastic partial differential equations

    CERN Document Server

    Chow, Pao-Liu

    2014-01-01

    Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad

  18. 一类具有非线性内部源和边界流的双重退化抛物型方程%Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

    Institute of Scientific and Technical Information of China (English)

    姜朝欣

    2007-01-01

    This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x + up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q > 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n+1)/ m+1}.

  19. Large Time Behavior of Solutions to Degenerate Parabolic Equations with Absorption%具吸附项退化抛物方程解的大时间渐近行为

    Institute of Scientific and Technical Information of China (English)

    高峰; 詹华税

    2006-01-01

    对如下形式的非线性抛物方程ut=up(△)(u(△)u)-uq,in Q∞=Ω×(0,∞)当p<1时,讨论了其解的大时间渐近性.%This article studies the large time asymptotic behavior of classical solution of a nonlinear parabolic equations of the following type ut = up(△) (u(△)u) - uq, inQ∞ = Ω × (0,∞) Where p < 1.

  20. 一类物方程的 H1-Galerkin混合有限元分析%The H1 -Galerkin Mixed Finite Element Analysis for A Class of Parabolic Equations

    Institute of Scientific and Technical Information of China (English)

    王琳

    2013-01-01

      The nonconforming H1 -Galerkin mixed finite element method is analyzed for a class of semilinear parabolic equations .The same optimal error estimates are obtained without using Ritz projec‐tion .%  文章利用 H1-Galerkin非协调混合元方法分析了一类半线性抛物方程,在不采用传统的Ritz投影的情况下得到了与协调有限元方法相同的收敛阶。

  1. Oscillations of the Solutions of Parabolic Partial Differential Equations of Neutral Type%非线性中立抛物型泛函微分方程解的振动判据

    Institute of Scientific and Technical Information of China (English)

    刘安平

    2000-01-01

    In this paper, we investigate oscillatory proper ties of solutions of certain parabolic partial differential equations and establ ish a series of sufficient conditions for oscillations of the equations. The res ults fully indicate that the oscillations are caused by delay. This is one impor tant conclusion and hence, reveals the essential differences between the equatio ns and those equations without delay.%讨论一类多滞量中立抛物型泛函微分方程解的振动性 质,获得了其一切解振动的充分条件及线性情况下的充要条件;指出了与普通抛物型偏微分 方程质的差异.

  2. Parabolic scaling beams.

    Science.gov (United States)

    Gao, Nan; Xie, Changqing

    2014-06-15

    We generalize the concept of diffraction free beams to parabolic scaling beams (PSBs), whose normalized intensity scales parabolically during propagation. These beams are nondiffracting in the circular parabolic coordinate systems, and all the diffraction free beams of Durnin's type have counterparts as PSBs. Parabolic scaling Bessel beams with Gaussian apodization are investigated in detail, their nonparaxial extrapolations are derived, and experimental results agree well with theoretical predictions.

  3. Controllability of nonlinear degenerate parabolic cascade systems

    Directory of Open Access Journals (Sweden)

    Mamadou Birba

    2016-08-01

    Full Text Available This article studies of null controllability property of nonlinear coupled one dimensional degenerate parabolic equations. These equations form a cascade system, that is, the solution of the first equation acts as a control in the second equation and the control function acts only directly on the first equation. We prove positive null controllability results when the control and a coupling set have nonempty intersection.

  4. On the dynamics of a mixed parabolic-gradient system

    NARCIS (Netherlands)

    J.K. Krottje (Johannes)

    2002-01-01

    textabstractIn the current paper the dynamics of a mixed parabolic-gradient system is examined. Thesystem, which is a coupled system of parabolic equations and gradient equations, acts as a first model for the outgrowth of axons in a developing nervous system. For modeling considerations it is relev

  5. Parabolic trough systems; Parabolrinnensysteme

    Energy Technology Data Exchange (ETDEWEB)

    Geyer, M. [Flabeg Solar International GmbH (Germany); Lerchenmueller, H.; Wittwer, V. [Fraunhofer ISE, Freiburg (Germany); Haeberle, A. [PSE GmbH (Germany); Luepfert, E.; Hennecke, K. [DLR, Koeln (Germany); Schiel, W. [SBP (Germany); Brakmann, G. [Fichtner Solar GmbH (Germany)

    2002-07-01

    The technology of parabolic trough power plants is presented: History, comparative assessment of different types of parabolic trough collectors, fresnel collectors, solar tracking systems, thermal efficiency, further research, performance of the SEGS parabolic trough power station in California. [German] Die Technik von Parabolrinnen-Kraftwerken wird vorgestellt: Entwicklungsgeschichte, Vergleich verschiedener Parabolrinnenkollektoren, fresnel kollektoren, Nachfuehrsysteme, thermischer Wirkungsgrad, weiterer Forschungsbedarf und Betriebserfahrung mit dem SEGS Parabolrinnenkraftwerk in Kalifornien. (uke)

  6. Controllable parabolic-cylinder optical rogue wave.

    Science.gov (United States)

    Zhong, Wei-Ping; Chen, Lang; Belić, Milivoj; Petrović, Nikola

    2014-10-01

    We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical simulations are performed for comparison with the analytical solutions and to confirm the stability of the rogue wave solution obtained. These optical rogue waves are built by the products of parabolic-cylinder functions and the basic rogue wave solution of the standard nonlinear Schrödinger equation. Such rogue waves may appear in different forms, as the hump and paw profiles.

  7. A nonlocal parabolic system with application to a thermoelastic problem

    Directory of Open Access Journals (Sweden)

    Y. Lin

    1999-01-01

    problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the results obtained in this paper.

  8. Flux form Semi-Lagrangian methods for parabolic problems

    CERN Document Server

    Bonaventura, Luca

    2015-01-01

    A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems.

  9. Measurement of Liquid Viscosities in Tapered or Parabolic Capillaries.

    Science.gov (United States)

    Ershov; Zorin; Starov

    1999-08-01

    The possibility of using tapered or parabolic capillaries for measurement of liquid viscosities is investigated both experimentally and theoretically. It is demonstrated that even small deviations in capillary radius from a constant value may substantially affect measurement results. Equations are derived which allow correct analysis of the measurement results in tapered or parabolic capillaries. The following cases are analyzed: a water imbibition into a tapered or parabolic capillary and displacement of one liquid by another immiscible liquid in tapered or parabolic capillaries. Two possibilities are considered: (a) the narrow end of the capillary as capillary inlet and (b) the wide end of the capillary as capillary inlet. Copyright 1999 Academic Press.

  10. Parabolic Dish Stirling Module

    Science.gov (United States)

    Washom, B.

    1984-01-01

    The design, manufacture, and assembly of a commercially designed parabolic dish Stirling 25 kWe module is examined. The cost, expected performance, design uniquenesses, and future commercial potential of this module, which is regarded as the most technically advanced in the parabolic dish industry is discussed.

  11. An H1-Galerkin Nonconforming Mixed Finite Element Method for Integro-Differential Equation of Parabolic Type%抛物型积分微分方程的非协调H1-Galerkin混合有限元方法

    Institute of Scientific and Technical Information of China (English)

    石东洋; 王海红

    2009-01-01

    H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.

  12. 具有不同初值的Dynamo抛物方程对初始时刻几何的连续依赖性%Continuous Dependence on the Initial-time Geometry for a Parabolic Equation from Dynamo Theory with Different Prescribed Data

    Institute of Scientific and Technical Information of China (English)

    陈展; 谭忠

    2005-01-01

    In this paper, we derive the continuous dependence on the initial-time geometry for the solution of a parabolic equation from dynamo theory. The forward in time problem and backward in time problem are considered. An explicit continuous dependence inequality is obtained even with different prescribed data.

  13. Nonlinear elliptic-parabolic problems

    CERN Document Server

    Kim, Inwon C

    2012-01-01

    We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are proved via the comparison principle. In particular, we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data. These results are new even in the linear case, where we also show that viscosity solutions coincide with the regular weak solutions introduced in [Alt&Luckhaus 1983].

  14. Oscillation of Solutions of Nonlinear Neutral Parabolic Differential Equations%非线性中立型抛物微分方程解的振动性

    Institute of Scientific and Technical Information of China (English)

    刘克英; 徐少贤; 刘安平

    2005-01-01

    This paper deals with the oscillatory properties of a class of nonlinear neutralparabolic partial differential equations with several delays. Sufficient criteria for the equa-tion to be oscillatory are obtained by making use of some results of first-order functionaldifferential inequalities. These results fully reveal the essential difference between this typeand that without delays.

  15. Manufacturing parabolic mirrors

    CERN Multimedia

    CERN PhotoLab

    1975-01-01

    The photo shows the construction of a vertical centrifuge mounted on an air cushion, with a precision of 1/10000 during rotation, used for the manufacture of very high=precision parabolic mirrors. (See Annual Report 1974.)

  16. Parabolic non-diffracting beams: geometrical approach

    Science.gov (United States)

    Sosa-Sánchez, Citlalli Teresa; Silva-Ortigoza, Gilberto; Alejandro Juárez-Reyes, Salvador; de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Julián-Macías, Israel; Ortega-Vidals, Paula

    2017-08-01

    The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this information, we compute the corresponding wavefronts and caustic, and find that qualitatively the caustic corresponds to the maximum of the intensity pattern and the wavefronts are deformations of conical surfaces.

  17. The parabolic trigonometric functions and the Chebyshev radicals

    OpenAIRE

    Dattoli, G.; Migliorati, M.; Ricci, P. E.

    2011-01-01

    The parabolic trigonometric functions have recently been introduced as an intermediate step between circular and hyperbolic functions. They have been shown to be expressible in terms of irrational functions, linked to the solution of third degree algebraic equations. We show the link of the parabolic trigonometric functions with the Chebyshev radicals and also prove that further generalized forms of trigonometric functions, providing the natural solutions of the quintic algebraic equation, ca...

  18. Two Splitting Positive Definite Mixed Element Methods for Pseudo-parabolic Equations%拟抛物方程的两类分裂正定混合元方法

    Institute of Scientific and Technical Information of China (English)

    郭会; 张建松

    2013-01-01

    In this paper,we establish two novel mixed finite element procedures for pseudo-parabolic equations.The resulting schemes can be split into two independent symmetric positive definite sub-schemes and does not need to solve a coupled system of equations.Optimal error estimates are proved in the framework of L2 (Ω) theory for u and H(div;Ω) theory for the unknown fluxσ without requiring the LBB consistency condition.Finally some numerical results are presented.%本文对拟抛物方程构造两种分裂对称正定混合元方法.通过适当选取变分形式,格式分裂成两个独立对称正定子格式,并且方法不需要验证LBB条件.收敛性分析表明方法关于变量u和引进的变量σ分别具有L 2(Ω)和H(div;Ω)范数意义下的最优收敛阶.最后,通过数值实验验证了方法的有效性.

  19. A short proof of increased parabolic regularity

    Directory of Open Access Journals (Sweden)

    Stephen Pankavich

    2015-08-01

    Full Text Available We present a short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates and an inductive method, can be extended to prove analogous results for problems with time-dependent coefficients, advection-diffusion or reaction diffusion equations, and nonlinear PDEs even when other tools, such as semigroup methods or the use of explicit fundamental solutions, are unavailable.

  20. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  1. Singular Solutions of the Cauchy Problem for Semilinear Parabolic Equations with Singular Potentions%具奇异位势的半线性抛物方程Cauchy问题的奇异解

    Institute of Scientific and Technical Information of China (English)

    曾有栋; 陈祖墀

    2002-01-01

    本文研究奇异半线性抛物方程ut-Δu+V1(x)u=V2(x)up,x∈Rn\{0},t>0的Cauchy问题解的存在性.这里,V1(x),V2(x)可以在原点具有奇性.利用Kato类函数和Green tight函数及不动点定理证明了问题存在正的奇异解,它在原点具有奇性.%In this paper we consider the Cauchy problem for the singular semilinear parabolic equation ut-Δu+V1(x)u=V2(x)up,x∈Rn\{0},t>0, where V1(x),V2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.

  2. Parabolic Strip Telescope

    CERN Document Server

    Chadzitaskos, Goce

    2013-01-01

    We present a proposal of a new type of telescopes using a rotating parabolic strip as the primary mirror. It is the most principal modification of the design of telescopes from the times of Galileo and Newton. In order to demonstrate the basic idea, the image of an artificial constellation observed by this kind of telescope was reconstructed using the techniques described in this article. As a working model of this new telescope, we have used an assembly of the primary mirror---a strip of acrylic glass parabolic mirror 40 cm long and 10 cm wid shaped as a parabolic cylinder of focal length 1 m---and an artificial constellation, a set of 5 apertures in a distance of 5 m illuminated from behind. In order to reconstruct the image, we made a series of snaps, each after a rotation of the constellation by 15 degrees. Using Matlab we reconstructed the image of the artificial constellation.

  3. Flux form Semi-Lagrangian methods for parabolic problems

    Directory of Open Access Journals (Sweden)

    Bonaventura Luca

    2016-09-01

    Full Text Available A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and stability analysis is proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection diffusion and nonlinear parabolic problems.

  4. Three-dimensional nonparaxial beams in parabolic rotational coordinates.

    Science.gov (United States)

    Deng, Dongmei; Gao, Yuanmei; Zhao, Juanying; Zhang, Peng; Chen, Zhigang

    2013-10-01

    We introduce a class of three-dimensional nonparaxial optical beams found in a parabolic rotational coordinate system. These beams, representing exact solutions of the nonparaxial Helmholtz equation, have inherent parabolic symmetries. Assisted with a computer-generated holography, we experimentally demonstrate the generation of different modes of these beams. The observed transverse beam patterns along the propagation direction agree well with those from our theoretical predication.

  5. Parabolic k-ample bundles

    CERN Document Server

    Biswas, Indranil

    2011-01-01

    We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the notion of a k-ample bundle, introduced by Sommese, to the context of parabolic bundles. A parabolic vector bundle $E_*$ is defined to be k-ample if the tautological line bundle ${\\mathcal O}_{{\\mathbb P}(E_*)}(1)$ is $k$--ample. We establish some properties of parabolic k-ample bundles.

  6. The 1D parabolic-parabolic Patlak-Keller-Segel model of chemotaxis: The particular integrable case and soliton solution

    Science.gov (United States)

    Shubina, Maria

    2016-09-01

    In this paper, we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.

  7. 二维非线性抛物型方程参数反演的贝叶斯推理估计%The estimated Bayesian inference of two-dimensional nonlinear parabolic equation parameter inversion

    Institute of Scientific and Technical Information of China (English)

    陈亚文; 邹学文

    2012-01-01

    为了克服观测数据有限以及数据存在一定误差对参数反演结果的影响,提出了一种参数反演的有效算法.根据已知参数的先验分布和已经获得的有误差的监测数据,以贝叶斯推理作为理论基础,获得参数的联合后验概率密度函数,再利用马尔科夫链蒙特卡罗模拟对后验分布进行采样,获得参数的后验边缘概率密度,由此得到了参数的数学期望等有效的统计量.数值模拟结果表明,此算法能够有效地解决二维非线性抛物型方程的参数识别反问题,且具有较高的精度.%In order to overcome the limited observation data with noise, an inversion of the effective parameters algorithm is presented. First, according to the parameters,a priori distribution and the limited observation data with noise, Bayesian inference as a theoretical foundation,parameters of the joint posterior probability density function are obtained. Markov chain Monte Carlo simulation was taken to sample the posterior distribution to get the marginal posterior probability function of the parameters, and the statistical quantities such as the mathematic expectation were calculated. Experimental results show that this algorithm can successfully solve the problem of two-dimensional nonlinear parabolic equation parameter inversion and inversion results have higher accuracy.

  8. Positive solutions of some parabolic system with cross-diffusion and nonlocal initial conditions

    CERN Document Server

    Walker, Christoph

    2010-01-01

    The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an age-structured predator-prey system with spatial dispersion. Based on unilateral global bifurcation methods for Fredholm operators and on maximal regularity for parabolic equations, global bifurcation of positive solutions is derived.

  9. equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1998-01-01

    Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

  10. Viscosity solutions of fully nonlinear functional parabolic PDE

    Directory of Open Access Journals (Sweden)

    Liu Wei-an

    2005-01-01

    Full Text Available By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.

  11. 抛物型G函数类的应用%APPLICATION OF THE G CLASS OF FUNCTIONS IN THE PARABOLIC CLASS

    Institute of Scientific and Technical Information of China (English)

    李胜宏

    2000-01-01

    In this paper,the application of the G class of functions in the parabolic class is con-sidered. The regularity of the solution for the first boundary value problem of parabolic equation in divergence form is proved.

  12. Session: Parabolic Troughs (Presentation)

    Energy Technology Data Exchange (ETDEWEB)

    Kutscher, C.

    2008-04-01

    The project description is R and D activities at NREL and Sandia aimed at lowering the delivered energy cost of parabolic trough collector systems and FOA awards to support industry in trought development. The primary objectives are: (1) support development of near-term parabolic trought technology for central station power generation; (2) support development of next-generation trought fields; and (3) support expansion of US trough industry. The major FY08 activities were: (1) improving reflector optics; (2) reducing receiver heat loss (including improved receiver coating and mitigating hydrogen accumulation); (3) measuring collector optical efficiency; (4) optimizing plant performance and reducing cost; (5) reducing plant water consumption; and (6) directly supporting industry needs, including FOA support.

  13. Parabolic Stein Manifolds

    CERN Document Server

    Aytuna, Aydin

    2011-01-01

    An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the first part of this note we compile these notions of parabolicity and give some immediate relations among them. In section 3 we relate some of these notions to the linear topological type of the Fr\\'echet space of analytic functions on the given manifold. In sections 4 and 5 we look at some examples and show, for example, that the complement of the zero set of a Weierstrass polynomial possesses a continuous plurisubharmonic exhaustion function that is maximal off a compact subset.

  14. Mahonians and parabolic quotients

    CERN Document Server

    Caselli, Fabrizio

    2011-01-01

    We study the distribution of the major index with sign on some parabolic quotients of the symmetric group, extending and generalizing simultaneously results of Panova [G. Panova, Bijective enumeration of permutations starting with a longest increasing subsequence, Discrete Math. Theor. Comput. Sci. Proc. AN (2010), 841--850], Gessel-Simion [M. Wachs, An involution for signed Eulerian numbers, Discrete Math. 99 (1992), 59--62] and Adin-Gessel-Roichman [R. Adin, I. Gessel and Y. Roichman, Signed Mahonians, J. Combin. Theory Ser. A 109 (2005), 25--43]. We further consider and compute the distribution of the flag-major index on some parabolic quotients of wreath products and other related groups. All these distributions turn out to have very simple factorization formulas.

  15. Reverberation Modelling Using a Parabolic Equation Method

    Science.gov (United States)

    2012-10-01

    et possiblement des échos de cibles. L’objet du présent contrat est une étude du recours à un modèle à équation parabolique, en particulier le...obtained by the ‘PE method’ were primarily compared to results obtained from a proprietary ray-based model provided by Brooke Numerical Services (BNS... Services . Target echo estimates are also compared to the BNS ray model result. In all cases but one the reference data is plotted as a solid red line

  16. Parabolic Wave Equation for Surface Water Waves.

    Science.gov (United States)

    1986-11-01

    extended to wave propagation problems in other fields of physical sciences, such as nonlinear optics ( Svelto , 1974), plasma physics (Karpman, 1975...34 Journal of Fluid Mechanics, Vol. 72, pp. 373-384. Svelto , 0., 1974, Progress in Optics, North-Holland Pub., Chapter 1, pp. 1-51. Tappert, F.D., 1977, "The

  17. Courant Algebroids in Parabolic Geometry

    CERN Document Server

    Armstrong, Stuart

    2011-01-01

    To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.

  18. The Parabolic Equation Model for Estimating Fog Attenuation at Millimeter Wavelengths%预测毫米波雾衰减的抛物方程模型研究

    Institute of Scientific and Technical Information of China (English)

    盛楠; 廖成; 张青洪; 陈伶璐; 周海京

    2014-01-01

    雾是影响毫米波通信系统性能的典型气象条件之一。针对传统经验模型无法精确预测多径效应下的电波传播问题,给出了基于抛物方程的雾衰减预测模型。以自由空间雾特征衰减的预测为例,将本文模型与Rayleigh近似及经验模型的计算结果进行对比,验证了该方法的可靠性。最后将该模型应用于预测35 GHz和94 GHz毫米波在分别含有平流雾和辐射雾的复杂环境中的传播特性,仿真结果表明该模型有效地反映了地形绕射、地表反射等对电波传播的影响,为快速准确地预测复杂地理环境及特殊气象条件中的电波传播特性提供了一种有效的预测模型。%Fog is one of the crucial factors in determining the performance of millimeter-wave communication systems .Be-cause of the fact that the multipath propagation is not be taken into account by the traditional empirical formulae ,this paper devel-oped a parabolic equation model for estimating fog attenuation .The fog attenuation rate predicted by the model agrees well with that obtained by the Rayleigh approximation and an empirical formula ,which verify the accuracy of our method .Finally ,the model is applied to simulate the propagation characteristics of millimeter-wave at frequency of 35 GHz and 94 GHz in Advection fog and Ra-diation fog with complex environments ,respectively .The results demonstrate that the model can take account of wave diffraction and reflection ,and thus our scheme provides an efficient numerical method for computation of the propagation characteristics of millime-ter-wave in complex environments .

  19. 非线性抛物积分微分方程的类Wilson非协调元分析%Analysis of Quasi-Wilson Nonconforming Element for Nonlinear Parabolic Integro-differential Equation

    Institute of Scientific and Technical Information of China (English)

    王芬玲; 石东洋; 陈金环

    2012-01-01

    在半离散和全离散格式下讨论非线性抛物积分微分方程的类Wilson非协调有限元逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该元的相容误差在能量模意义下可以达到O(h2 )/O(h3)比其插值误差高一阶和二阶的特殊性质,再结合协调部分的高精度分析及插值后处理技术,并借助于双线性插值代替传统有限元分析中不可缺少的Ritz-Volterra投影导出了半离散格式下的O(h2)阶超逼近和超收敛结果.同时分别得到了向后Euler全离散格式下的超逼近性和Crank-Nicolson全离散格式下的最优误差估计.%A nonconforming quasi-Wilson finite element approximation for nonlinear parabolic integro-differential equation is discussed under the semi-discrete and fully-discrete schemes. By use of the special property of the element,i. e. , the consistence error estimate in energy norm when the exact solution u of the problem belongs to H3(Ω)/ H4(Ω) can reach to O(h2)/O(h3), one/two order higher than the interpolation error, then combination it with the higher accuracy analysis of its conforming part and the interpolated postprocessing technique, the superclose and superconvergence results with order O(h2) are obtained for semi-discrete scheme through interpolation instead of the Ritz-Volterra projection which is an indispensable tool in traditional finite element analysis. The superclose property and the optimal error estimate for backward Euler and Crank-Nicolson fully-discrete schemes are derived , respectively.

  20. Monte Carlo method for solving a parabolic problem

    Directory of Open Access Journals (Sweden)

    Tian Yi

    2016-01-01

    Full Text Available In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.

  1. Discrete approximations for singularly perturbed boundary value problems with parabolic layers

    NARCIS (Netherlands)

    Farrell, P.A.; Hemker, P.W.; Shishkin, G.I.

    1995-01-01

    Singularly perturbed boundary value problems for equations of elliptic and parabolic type are studied. For small values of the perturbation parameter, parabolic boundary layers appear in these problems. If classical discretisation methods are used, the solution of the finite difference scheme and th

  2. Fabrication and characterization of non-linear parabolic microporous membranes.

    Science.gov (United States)

    Rajasekaran, Pradeep Ramiah; Sharifi, Payam; Wolff, Justin; Kohli, Punit

    2015-01-01

    Large scale fabrication of non-linear microporous membranes is of technological importance in many applications ranging from separation to microfluidics. However, their fabrication using traditional techniques is limited in scope. We report on fabrication and characterization of non-linear parabolic micropores (PMS) in polymer membranes by utilizing flow properties of fluids. The shape of the fabricated PMS corroborated well with simplified Navier-Stokes equation describing parabolic relationship of the form L - t(1/2). Here, L is a measure of the diameter of the fabricated micropores during flow time (t). The surface of PMS is smooth due to fluid surface tension at fluid-air interface. We demonstrate fabrication of PMS using curable polydimethylsiloxane (PDMS). The parabolic shape of micropores was a result of interplay between horizontal and vertical fluid movements due to capillary, viscoelastic, and gravitational forces. We also demonstrate fabrication of asymmetric "off-centered PMS" and an array of PMS membranes using this simple fabrication technique. PMS containing membranes with nanoscale dimensions are also possible by controlling the experimental conditions. The present method provides a simple, easy to adopt, and energy efficient way for fabricating non-linear parabolic shape pores at microscale. The prepared parabolic membranes may find applications in many areas including separation, parabolic optics, micro-nozzles / -valves / -pumps, and microfluidic and microelectronic delivery systems.

  3. Identification of Plasmonic Modes in Parabolic Cylinder Geometry by Quasi-Separation of Variables.

    Science.gov (United States)

    Kurihara, Kazuyoshi; Otomo, Akira; Yamamoto, Kazuhiro; Takahara, Junichi; Tani, Masahiko; Kuwashima, Fumiyoshi

    This paper describes the plasmonic modes in the parabolic cylinder geometry as a theoretical complement to the previous paper (J Phys A 42:185401) that considered the modes in the circular paraboloidal geometry. In order to identify the plasmonic modes in the parabolic cylinder geometry, analytic solutions for surface plasmon polaritons are examined by solving the wave equation for the magnetic field in parabolic cylindrical coordinates using quasi-separation of variables in combination with perturbation methods. The examination of the zeroth-order perturbation equations showed that solutions cannot exist for the parabolic metal wedge but can be obtained for the parabolic metal groove as standing wave solutions indicated by the even and odd symmetries.

  4. A parabolic singular perturbation problem with an internal layer

    NARCIS (Netherlands)

    Grasman, J.; Shih, S.D.

    2004-01-01

    A method is presented to approximate with singular perturbation methods a parabolic differential equation for the quarter plane with a discontinuity at the corner. This discontinuity gives rise to an internal layer. It is necessary to match the local solution in this layer with the one in a corner l

  5. LEAST-SQUARES MIXED FINITE ELEMENT METHODS FOR NONLINEAR PARABOLIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Dan-ping Yang

    2002-01-01

    Two least-squares mixed finite element schemes are formulated to solve the initialboundary value problem of a nonlinear parabolic partial differential equation and the convergence of these schemes are analyzed.

  6. Commercialization of parabolic dish systems

    Science.gov (United States)

    Washom, B.

    1982-01-01

    The impact of recent federal tax and regulatory legislation on the commercialization of parabolic solar reflector technology is assessed. Specific areas in need of technical or economic improvement are noted.

  7. The planar parabolic optical antenna.

    Science.gov (United States)

    Schoen, David T; Coenen, Toon; García de Abajo, F Javier; Brongersma, Mark L; Polman, Albert

    2013-01-09

    One of the simplest and most common structures used for directing light in macroscale applications is the parabolic reflector. Parabolic reflectors are ubiquitous in many technologies, from satellite dishes to hand-held flashlights. Today, there is a growing interest in the use of ultracompact metallic structures for manipulating light on the wavelength scale. Significant progress has been made in scaling radiowave antennas to the nanoscale for operation in the visible range, but similar scaling of parabolic reflectors employing ray-optics concepts has not yet been accomplished because of the difficulty in fabricating nanoscale three-dimensional surfaces. Here, we demonstrate that plasmon physics can be employed to realize a resonant elliptical cavity functioning as an essentially planar nanometallic structure that serves as a broadband unidirectional parabolic antenna at optical frequencies.

  8. Parabolic sheaves on logarithmic schemes

    OpenAIRE

    Borne, Niels; Vistoli, Angelo

    2010-01-01

    We show how the natural context for the definition of parabolic sheaves on a scheme is that of logarithmic geometry. The key point is a reformulation of the concept of logarithmic structure in the language of symmetric monoidal categories, which might be of independent interest. Our main result states that parabolic sheaves can be interpreted as quasi-coherent sheaves on certain stacks of roots.

  9. Parabolic metamaterials and Dirac bridges

    Science.gov (United States)

    Colquitt, D. J.; Movchan, N. V.; Movchan, A. B.

    2016-10-01

    A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.

  10. Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

    Science.gov (United States)

    Smith, A. W.; Brennan, K. F.

    1996-01-01

    Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

  11. Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

    Science.gov (United States)

    Smith, A. W.; Brennan, K. F.

    1996-01-01

    Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

  12. Parabolic aircraft solidification experiments

    Science.gov (United States)

    Workman, Gary L. (Principal Investigator); Smith, Guy A.; OBrien, Susan

    1996-01-01

    A number of solidification experiments have been utilized throughout the Materials Processing in Space Program to provide an experimental environment which minimizes variables in solidification experiments. Two techniques of interest are directional solidification and isothermal casting. Because of the wide-spread use of these experimental techniques in space-based research, several MSAD experiments have been manifested for space flight. In addition to the microstructural analysis for interpretation of the experimental results from previous work with parabolic flights, it has become apparent that a better understanding of the phenomena occurring during solidification can be better understood if direct visualization of the solidification interface were possible. Our university has performed in several experimental studies such as this in recent years. The most recent was in visualizing the effect of convective flow phenomena on the KC-135 and prior to that were several successive contracts to perform directional solidification and isothermal casting experiments on the KC-135. Included in this work was the modification and utilization of the Convective Flow Analyzer (CFA), the Aircraft Isothermal Casting Furnace (ICF), and the Three-Zone Directional Solidification Furnace. These studies have contributed heavily to the mission of the Microgravity Science and Applications' Materials Science Program.

  13. In-plane elastic stability of fixed parabolic shallow arches

    Institute of Scientific and Technical Information of China (English)

    CAI JianGuo; FENG Jian; CHEN Yao; HUANG LiFeng

    2009-01-01

    The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves-tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym-metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposedto simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch's modified slenderness.

  14. In-plane elastic stability of fixed parabolic shallow arches

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym- metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness.

  15. Analysis and conceptual design of a lunar radiator parabolic shade

    Science.gov (United States)

    Ewert, Michael K.; Clark, Craig S.

    1991-01-01

    On the moon, the available heat sink temperature for a vertical unshaded radiator at the equator is 322 K. A method of reducing this heat sink temperature using a parabolic trough shading device was investigated. A steady state heat balance was performed to predict the available heat sink temperature. The effect of optical surface properties on system performance was investigated. Various geometric configurations were also evaluated. A flexible shade conceptual design is presented which greatly reduces the weight and stowed volume of the system. The concept makes use of the natural catenary shape assumed by a flexible material when supported at two points. The catenary shape is very near parabolic. The lunar radiator parabolic shade design presented integrates the energy collection and rejection of a solar dynamic power cycle with the moderate temperature waste heat rejection of a lunar habitat.

  16. Engineering parabolic beams with dynamic intensity profiles.

    Science.gov (United States)

    Ruelas, Adrian; Lopez-Aguayo, Servando; Gutiérrez-Vega, Julio C

    2013-08-01

    We present optical fields formed by superposing nondiffracting parabolic beams with distinct longitudinal wave-vector components, generating light profiles that display intensity fluxes following parabolic paths in the transverse plane. Their propagation dynamics vary depending on the physical mechanism originating interference, where the possibilities include constructive and destructive interference between traveling parabolic beams, interference between stationary parabolic modes, and combinations of these. The dark parabolic region exhibited by parabolic beams permits a straightforward superposition of intensity fluxes, allowing formation of a variety of profiles, which can exhibit circular, elliptic, and other symmetries.

  17. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  18. Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth

    Institute of Scientific and Technical Information of China (English)

    Shang-bin Cui; Xue-mei Wei

    2005-01-01

    In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a nonlinear second-order parabolic equation describing the diffusion of nutrient in the tumor, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells, respectively. By applying Lp theory of parabolic equations, the characteristic theory of hyperbolic equations, and the Banach fixed point theorem, we prove that this problem has a unique global classical solution.

  19. The Blow-up Rate for Positive Solutions of Indefinite Parabolic Problems and Related Liouville Type Theorems

    Institute of Scientific and Technical Information of China (English)

    Ruixiang XING

    2009-01-01

    In this paper,we derive an upper bound estimate of the blow-up rate for positive solutions of indefinite parabolic equations from Liouville type theorems. We also use moving plane method to prove the related Liouville type theorems for semilinear parabolic problems.

  20. Shenandoah parabolic dish solar collector

    Energy Technology Data Exchange (ETDEWEB)

    Kinoshita, G.S.

    1985-01-01

    The objectives of the Shenandoah, Georgia, Solar Total Energy System are to design, construct, test, and operate a solar energy system to obtain experience with large-scale hardware systems for future applications. This report describes the initial design and testing activities conducted to select and develop a collector that would serve the need of such a solar total energy system. The parabolic dish was selected as the collector most likely to maximize energy collection as required by this specific site. The fabrication, testing, and installation of the parabolic dish collector incorporating improvements identified during the development testing phase are described.

  1. Shenandoah parabolic dish solar collector

    Energy Technology Data Exchange (ETDEWEB)

    Kinoshita, G.S.

    1985-01-01

    The objectives of the Shenandoah, Georgia, Solar Total Energy System are to design, construct, test, and operate a solar energy system to obtain experience with large-scale hardware systems for future applications. This report describes the initial design and testing activities conducted to select and develop a collector that would serve the need of such a solar total energy system. The parabolic dish was selected as the collector most likely to maximize energy collection as required by this specific site. The fabrication, testing, and installation of the parabolic dish collector incorporating improvements identified during the development testing phase are described.

  2. Self-similar parabolic plasmonic beams.

    Science.gov (United States)

    Davoyan, Arthur R; Turitsyn, Sergei K; Kivshar, Yuri S

    2013-02-15

    We demonstrate that an interplay between diffraction and defocusing nonlinearity can support stable self-similar plasmonic waves with a parabolic profile. Simplicity of a parabolic shape combined with the corresponding parabolic spatial phase distribution creates opportunities for controllable manipulation of plasmons through a combined action of diffraction and nonlinearity.

  3. Renormalizing Partial Differential Equations

    OpenAIRE

    Bricmont, J.; Kupiainen, A.

    1994-01-01

    In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.

  4. Plane and parabolic solar panels

    CERN Document Server

    Sales, J H O

    2009-01-01

    We present a plane and parabolic collector that absorbs radiant energy and transforms it in heat. Therefore we have a panel to heat water. We study how to increment this capture of solar beams onto the panel in order to increase its efficiency in heating water.

  5. Parabolic tapers for overmoded waveguides

    Science.gov (United States)

    Doane, J.L.

    1983-11-25

    A waveguide taper with a parabolic profile, in which the distance along the taper axis varies as the square of the tapered dimension, provides less mode conversion than equal length linear tapers and is easier to fabricate than other non-linear tapers.

  6. Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory

    OpenAIRE

    M. Jakomin; Kosel, F.

    2011-01-01

    In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the lar...

  7. Parabolic dish reflectors for solar applications approximated by simple surfaces

    OpenAIRE

    Broman, Lars; Broman, Arne

    1996-01-01

    Two different concentrating mirrors have been constructed that resemble parabolic dish reflectors. Both mirrors are made of slightly curved strips of flat, bendable material. The strips of the most simplified mirror have only large-radius circles and straight lines as boundaries. The necessary equations for making the mirrors have been derived. Also a simple way to make a stiff, lightweight frame and support for the mirror strips has been developed. Models of the mirrors have been built and s...

  8. Gradient estimates for parabolic and elliptic systems from linear laminates

    CERN Document Server

    Dong, Hongjie

    2012-01-01

    We establish several gradient estimates for second-order divergence type parabolic and elliptic systems. The coefficients and data are assumed to be H\\"older or Dini continuous in the time variable and all but one spatial variables. This type of systems arises from the problems of linearly elastic laminates and composite materials. For the proof, we use Campanato's approach in a novel way. Non-divergence type equations under a similar condition are also discussed.

  9. Theoretical analysis of a parabolic torus reflector antenna with multibeam

    Institute of Scientific and Technical Information of China (English)

    杜彪; 杨可忠; 钟顺时

    1995-01-01

    The parametric equations and the formulas of unit normal vector and surface element for aparabolic torus reflector antenna are derived and the mechanism of producing multibeam is proposed, Based on physical optics, the radiation pattern formulas for the antenna are given, with which the effects of geometric parameters on the antenna are studied. The good agreement between the calculated patterns and the measured ones shows that the theory is helpful for designing parabolic torus antennas.

  10. Proton driven plasma wakefield generation in a parabolic plasma channel

    Science.gov (United States)

    Golian, Y.; Dorranian, D.

    2016-11-01

    An analytical model for the interaction of charged particle beams and plasma for a wakefield generation in a parabolic plasma channel is presented. In the suggested model, the plasma density profile has a minimum value on the propagation axis. A Gaussian proton beam is employed to excite the plasma wakefield in the channel. While previous works investigated on the simulation results and on the perturbation techniques in case of laser wakefield accelerations for a parabolic channel, we have carried out an analytical model and solved the accelerating field equation for proton beam in a parabolic plasma channel. The solution is expressed by Whittaker (hypergeometric) functions. Effects of plasma channel radius, proton bunch parameters and plasma parameters on the accelerating processes of proton driven plasma wakefield acceleration are studied. Results show that the higher accelerating fields could be generated in the PWFA scheme with modest reductions in the bunch size. Also, the modest increment in plasma channel radius is needed to obtain maximum accelerating gradient. In addition, the simulations of longitudinal and total radial wakefield in parabolic plasma channel are presented using LCODE. It is observed that the longitudinal wakefield generated by the bunch decreases with the distance behind the bunch while total radial wakefield increases with the distance behind the bunch.

  11. Curvilinear parabolic approximation for surface wave transformation with wave current interaction

    Science.gov (United States)

    Shi, Fengyan; Kirby, James T.

    2005-04-01

    The direct coordinate transformation method, which only transforms independent variables and retains Cartesian dependent variables, may not be an appropriate method for the purpose of simplifying the curvilinear parabolic approximation of the vector form of the wave-current equation given by Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. In this paper, the covariant-contravariant tensor method is used for the curvilinear parabolic approximation. We use the covariant components of the wave number vector and contravariant components of the current velocity vector so that the derivation of the curvilinear equation closely follows the higher-order approximation in rectangular Cartesian coordinates in Kirby [Higher-order approximations in the parabolic equation method for water waves, J. Geophys. Res. 91 (1986) 933-952]. The resulting curvilinear equation can be easily implemented using the existing model structure and numerical schemes adopted in the Cartesian parabolic wave model [J.T. Kirby, R.A. Dalrymple, F. Shi, Combined Refraction/Diffraction Model REF/DIF 1, Version 2.6. Documentation and User's Manual, Research Report, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, 2004]. Several examples of wave simulations in curvilinear coordinate systems, including a case with wave-current interaction, are shown with comparisons to theoretical solutions or measurement data.

  12. Analyzing Parabolic Profile Path for Underwater Towed-Cable

    Institute of Scientific and Technical Information of China (English)

    Vineet KSrivastava

    2014-01-01

    This article discusses the dynamic state analysis of underwater towed-cable when tow-ship changes its speed in a direction making parabolic profile path. A three-dimensional model of underwater towed system is studied. The established governing equations for the system have been solved using the central implicit finite-difference method. The obtained difference non-linear coupled equations are solved by Newton’s method and satisfactory results were achieved. The solution of this problem has practical importance in the estimation of dynamic loading and motion, and hence it is directly applicable to the enhancement of safety and the effectiveness of the offshore activities.

  13. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA

  14. Comprehensive analysis of passive generation of parabolic similaritons in tapered hydrogenated amorphous silicon photonic wires.

    Science.gov (United States)

    Mei, Chao; Li, Feng; Yuan, Jinhui; Kang, Zhe; Zhang, Xianting; Yan, Binbin; Sang, Xinzhu; Wu, Qiang; Zhou, Xian; Zhong, Kangping; Wang, Liang; Wang, Kuiru; Yu, Chongxiu; Wai, P K A

    2017-06-19

    Parabolic pulses have important applications in both basic and applied sciences, such as high power optical amplification, optical communications, all-optical signal processing, etc. The generation of parabolic similaritons in tapered hydrogenated amorphous silicon photonic wires at telecom (λ ~ 1550 nm) and mid-IR (λ ≥ 2100 nm) wavelengths is demonstrated and analyzed. The self-similar theory of parabolic pulse generation in passive waveguides with increasing nonlinearity is presented. A generalized nonlinear Schrödinger equation is used to describe the coupled dynamics of optical field in the tapered hydrogenated amorphous silicon photonic wires with either decreasing dispersion or increasing nonlinearity. The impacts of length dependent higher-order effects, linear and nonlinear losses including two-photon absorption, and photon-generated free carriers, on the pulse evolutions are characterized. Numerical simulations show that initial Gaussian pulses will evolve into the parabolic pulses in the waveguide taper designed.

  15. Stochastic differential equations and applications

    CERN Document Server

    Friedman, Avner

    2006-01-01

    This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es

  16. Distribution-valued weak solutions to a parabolic problem arising in financial mathematics

    Directory of Open Access Journals (Sweden)

    Michael Eydenberg

    2009-07-01

    Full Text Available We study distribution-valued solutions to a parabolic problem that arises from a model of the Black-Scholes equation in option pricing. We give a minor generalization of known existence and uniqueness results for solutions in bounded domains $Omega subset mathbb{R}^{n+1}$ to give existence of solutions for certain classes of distributions $fin mathcal{D}'(Omega$. We also study growth conditions for smooth solutions of certain parabolic equations on $mathbb{R}^nimes (0,T$ that have initial values in the space of distributions.

  17. A multiplicity result for a class of quasilinear elliptic and parabolic problems

    Directory of Open Access Journals (Sweden)

    M. R. Grossinho

    1997-04-01

    Full Text Available We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive of the nonlinearity at the right-hand side oscillates at infinity. The proof is based on the construction of upper and lower solutions, which are obtained as solutions of suitable comparison equations. This method allows the introduction of conditions on the potential for the study of parabolic problems, as well as to treat simultaneously the singular and the degenerate case.

  18. Three-dimensional rogue waves in nonstationary parabolic potentials.

    Science.gov (United States)

    Yan, Zhenya; Konotop, V V; Akhmediev, N

    2010-09-01

    Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1) -dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1) -dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1) -dimensional case to the variety of solutions of integrable NLS equation of the (1+1) -dimensional case. As an example, we illustrated our technique using two lowest-order rational solutions of the NLS equation as seeding functions to obtain rogue wavelike solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wavelike solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and Bose-Einstein condensates.

  19. Fokker-Planck-Kolmogorov equations

    CERN Document Server

    Bogachev, Vladimir I; Röckner, Michael; Shaposhnikov, Stanislav V

    2015-01-01

    This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

  20. A Nonconforming H1-Galerkin Expanded Mixed Finite Element Method for Semilinear Parabolic Partial Differential Equations%拟线性抛物问题的非协调 H1-Galerkin扩展混合有限元方法∗

    Institute of Scientific and Technical Information of China (English)

    石东洋; 郭城; 王海红

    2013-01-01

      抛物方程在热的传导、溶质的弥散以及多孔介质的渗流等问题中有着广泛的应用。本文综合 H1-Galerkin 混合有限元方法与扩展混合有限元方法的优点,针对一类拟线性抛物问题,提出了在半离散和向后的 Euler 全离散格式下非协调的 H1-Galerkin 扩展混合有限元方法。该方法利用真解的插值,不需要利用投影,从而得到有限元解的存在唯一性和格式的稳定性,以及和以往协调元相同的误差估计。%The parabolic partial differential equations have wide range of applications in the heat transmission, the solute dissemination, porous media seepage and so on. In this paper, the nonconforming Galerkin expanded finite element method for a class of quasi-linear partial dif-ferential equations is proposed both for semi-discrete and back-ward Euler full discrete schemes by applying the advantages of Galerkin mixed finite element method and expanded finite ele-ment method. The same error estimates as the conforming case in the previous literature, the existence and uniqueness of the finite element solutions and the stability of the schemes are obtained by means of the interpolation of the true solutions instead of projections.

  1. Asymptotic Properties of Parabolic Systems for Null-Recurrent Switching Diffusions

    Institute of Scientific and Technical Information of China (English)

    R.Z.Khasminskii; C.Zhu; G.Yin

    2007-01-01

    This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions,which are diffusion processes modulated by continuous-time Markov chains.A sufficient condition for null recurrence is presented.Moreover,convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established.Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain.To verify the condition,boundary value problems(BVPs)for parabolic systems are treated,which are not the usual two-point BVP type.An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.

  2. Convergence of shock waves between conical and parabolic boundaries

    Science.gov (United States)

    Yanuka, D.; Zinowits, H. E.; Antonov, O.; Efimov, S.; Virozub, A.; Krasik, Ya. E.

    2016-07-01

    Convergence of shock waves, generated by underwater electrical explosions of cylindrical wire arrays, between either parabolic or conical bounding walls is investigated. A high-current pulse with a peak of ˜550 kA and rise time of ˜300 ns was applied for the wire array explosion. Strong self-emission from an optical fiber placed at the origin of the implosion was used for estimating the time of flight of the shock wave. 2D hydrodynamic simulations coupled with the equations of state of water and copper showed that the pressure obtained in the vicinity of the implosion is ˜7 times higher in the case of parabolic walls. However, comparison with a spherical wire array explosion showed that the pressure in the implosion vicinity in that case is higher than the pressure in the current experiment with parabolic bounding walls because of strong shock wave reflections from the walls. It is shown that this drawback of the bounding walls can be significantly minimized by optimization of the wire array geometry.

  3. On the solution of Liouville equation

    CERN Document Server

    Menotti, Pietro

    2016-01-01

    We give a short and rigorous proof of the existence and uniqueness of the solution of Liouville equation with sources, both elliptic and parabolic, on the sphere and on all higher genus compact Riemann surfaces.

  4. Efficient Method for Calculating the Composite Stiffness of Parabolic Leaf Springs with Variable Stiffness for Vehicle Rear Suspension

    OpenAIRE

    Wen-ku Shi; Cheng Liu; Zhi-yong Chen; Wei He; Qing-hua Zu

    2016-01-01

    The composite stiffness of parabolic leaf springs with variable stiffness is difficult to calculate using traditional integral equations. Numerical integration or FEA may be used but will require computer-aided software and long calculation times. An efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness is developed and evaluated to reduce the complexity of calculation and shorten the calculation time. A simplified model for double-leaf spr...

  5. Theoretical Study of the Compound Parabolic Trough Solar Collector

    Directory of Open Access Journals (Sweden)

    Dr. Subhi S. Mahammed

    2012-06-01

    Full Text Available Theoretical design of compound parabolic trough solar collector (CPC without tracking is presented in this work. The thermal efficiency is obtained by using FORTRAN 90 program. The thermal efficiency is between (60-67% at mass flow rate between (0.02-0.03 kg/s at concentration ratio of (3.8 without need to tracking system.The total and diffused radiation is calculated for Tikrit city by using theoretical equations. Good agreement between present work and the previous work.

  6. Space-time isogeometric analysis of parabolic evolution problems

    Science.gov (United States)

    Langer, Ulrich; Moore, Stephen E.; Neumüller, Martin

    2016-07-01

    We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.

  7. Properties of positive solutions to a nonlinear parabolic problem

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.

  8. Deterministic homogenization of parabolic monotone operators with time dependent coefficients

    Directory of Open Access Journals (Sweden)

    Gabriel Nguetseng

    2004-06-01

    Full Text Available We study, beyond the classical periodic setting, the homogenization of linear and nonlinear parabolic differential equations associated with monotone operators. The usual periodicity hypothesis is here substituted by an abstract deterministic assumption characterized by a great relaxation of the time behaviour. Our main tool is the recent theory of homogenization structures by the first author, and our homogenization approach falls under the two-scale convergence method. Various concrete examples are worked out with a view to pointing out the wide scope of our approach and bringing the role of homogenization structures to light.

  9. Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities

    Science.gov (United States)

    Li, Xiaojun

    2016-08-01

    In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .

  10. Time-optimal control of infinite order distributed parabolic systems involving time lags

    Directory of Open Access Journals (Sweden)

    G.M. Bahaa

    2014-06-01

    Full Text Available A time-optimal control problem for linear infinite order distributed parabolic systems involving constant time lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.

  11. Finite difference method for the reverse parabolic problem with Neumann condition

    Science.gov (United States)

    Ashyralyyev, Charyyar; Dural, Ayfer; Sozen, Yasar

    2012-08-01

    A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Neumann condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

  12. An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions

    Directory of Open Access Journals (Sweden)

    Ioan Bejenaru

    2001-07-01

    Full Text Available In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to nonlinear, possible non monotone, dynamic boundary conditions.

  13. Stability of Difference Schemes for Fractional Parabolic PDE with the Dirichlet-Neumann Conditions

    Directory of Open Access Journals (Sweden)

    Zafer Cakir

    2012-01-01

    boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln (1/(+|ℎ| for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.

  14. ROS3P : an accurate third-order Rosenbrock solver designed for parabolic problems

    NARCIS (Netherlands)

    Lang, J.; Verwer, J.G.

    2000-01-01

    In this note we present a new Rosenbrock solver which is third--order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reductions when they are applied to partial differential equations, additional order conditions have to be satisfied. Although these conditions

  15. On a Parabolic-Elliptic system with chemotaxis and logistic type growth

    Science.gov (United States)

    Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio

    2016-10-01

    We consider a nonlinear PDEs system of two equations of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a biological population "u" towards a higher concentration of a chemical agent "w" in a bounded and regular domain Ω ⊂RN for arbitrary N ∈ N. After normalization, the system is as follows

  16. Analysis of the Quality of Parabolic Flight

    Science.gov (United States)

    Lambot, Thomas; Ord, Stephan F.

    2016-01-01

    Parabolic flights allow researchers to conduct several 20 second micro-gravity experiments in the course of a single day. However, the measurement can have large variations over the course of a single parabola, requiring the knowledge of the actual flight environment as a function of time. The NASA Flight Opportunities program (FO) reviewed the acceleration data of over 400 parabolic flights and investigated the quality of micro-gravity for scientific purposes. It was discovered that a parabolic flight can be segmented into multiple parts of different quality and duration, a fact to be aware of when planning an experiment.

  17. 2-dimensional Radical Symmetric Solutions for Modified Landau-Lifshitz Equation

    Institute of Scientific and Technical Information of China (English)

    曾明

    2006-01-01

    @@ Landau-Lifshitz equation is a nonlinear parabolic equation describing micromagnetic evolution[1]. In [2] A. Visintin proposed a modified Landau-Lifshitz equation to account for dry friction in domain-wall displacement due to magnetic inclusion, which reads

  18. On explicit and numerical solvability of parabolic initial-boundary value problems

    Directory of Open Access Journals (Sweden)

    Lepsky Olga

    2006-01-01

    Full Text Available A homogeneous boundary condition is constructed for the parabolic equation in an arbitrary cylindrical domain ( being a bounded domain, and being the identity operator and the Laplacian which generates an initial-boundary value problem with an explicit formula of the solution . In the paper, the result is obtained not just for the operator , but also for an arbitrary parabolic differential operator , where is an elliptic operator in of an even order with constant coefficients. As an application, the usual Cauchy-Dirichlet boundary value problem for the homogeneous equation in is reduced to an integral equation in a thin lateral boundary layer. An approximate solution to the integral equation generates a rather simple numerical algorithm called boundary layer element method which solves the 3D Cauchy-Dirichlet problem (with three spatial variables.

  19. Reflective Properties of a Parabolic Mirror.

    Science.gov (United States)

    Ramsey, Gordon P.

    1991-01-01

    An incident light ray parallel to the optical axis of a parabolic mirror will be reflected at the focal point and vice versa. Presents a mathematical proof that uses calculus, algebra, and geometry to prove this reflective property. (MDH)

  20. CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

    Institute of Scientific and Technical Information of China (English)

    Xinlong FENG; Yinnian HE

    2016-01-01

    In this paper, the Crank-Nicolson/Newton scheme for solving numerically second-order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nicolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank-Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the effcient performance of the proposed scheme.

  1. Self-similar propagation and amplification of parabolic pulses in optical fibers.

    Science.gov (United States)

    Fermann, M E; Kruglov, V I; Thomsen, B C; Dudley, J M; Harvey, J D

    2000-06-26

    Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

  2. Optimal boundary control of parabolic system on doubly connected region in new space

    Institute of Scientific and Technical Information of China (English)

    陈任昭

    1995-01-01

    The optimal boundary control of the system governed by parabolic partial differential equations on a doubly connected region in the new space advanced by Lions is discussed. It proves the necessary and sufficient conditions for a control to be optimal and obtains the optimality system consisting of partial differential equations and variational inequalities. And the application of penalty shifting method to the approximate solution of control problems for the system is researched.

  3. Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions

    Science.gov (United States)

    Pao, C. V.; Ruan, W. H.

    2007-09-01

    The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.

  4. Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition

    Science.gov (United States)

    Pao, C. V.; Ruan, W. H.

    Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.

  5. Steadily translating parabolic dissolution fingers

    CERN Document Server

    Kondratiuk, Paweł

    2015-01-01

    Dissolution fingers (or wormholes) are formed during the dissolution of a porous rock as a result of nonlinear feedbacks between the flow, transport and chemical reactions at pore surfaces. We analyze the shapes and growth velocities of such fingers within the thin-front approximation, in which the reaction is assumed to take place instantaneously with the reactants fully consumed at the dissolution front. We concentrate on the case when the main flow is driven by the constant pressure gradient far from the finger, and the permeability contrast between the inside and the outside of the finger is finite. Using Ivantsov ansatz and conformal transformations we find the family of steadily translating fingers characterized by a parabolic shape. We derive the reactant concentration field and the pressure field inside and outside of the fingers and show that the flow within them is uniform. The advancement velocity of the finger is shown to be inversely proportional to its radius of curvature in the small P\\'{e}clet...

  6. Time-parallel iterative methods for parabolic PDES: Multigrid waveform relaxation and time-parallel multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Vandewalle, S. [Caltech, Pasadena, CA (United States)

    1994-12-31

    Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.

  7. Difference schemes for fully nonlinear pseudo-parabolic systems with two space dimensions

    Institute of Scientific and Technical Information of China (English)

    周毓麟; 袁光伟

    1996-01-01

    The first boundary value problem for the fully nonlinear pseudoparabolic systems of partial differential equations with two space dimensions by the finite difference method is studied. The existence and uniqueness of the discrete vector solutions for the difference systems are established by the fixed point technique. The stability and convergence of the discrete vector solutions of the difference schemes to the vector solutions of the original boundary problem of the fully nonlinear pseudo-parabolic system are obtained by way of a priori estimation. Here the unique smooth vector solution of the original problems for the fully nonlinear pseudo-parabolic system is assumed. Moreover, by the method used here, it can be proved that analogous results hold for fully nonlinear pseudo-parabolic system with three space dimensions, and improve the known results in the case of one space dimension.

  8. Extending the Utility of the Parabolic Approximation in Medical Ultrasound Using Wide-Angle Diffraction Modeling.

    Science.gov (United States)

    Soneson, Joshua E

    2017-04-01

    Wide-angle parabolic models are commonly used in geophysics and underwater acoustics but have seen little application in medical ultrasound. Here, a wide-angle model for continuous-wave high-intensity ultrasound beams is derived, which approximates the diffraction process more accurately than the commonly used Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation without increasing implementation complexity or computing time. A method for preventing the high spatial frequencies often present in source boundary conditions from corrupting the solution is presented. Simulations of shallowly focused axisymmetric beams using both the wide-angle and standard parabolic models are compared to assess the accuracy with which they model diffraction effects. The wide-angle model proposed here offers improved focusing accuracy and less error throughout the computational domain than the standard parabolic model, offering a facile method for extending the utility of existing KZK codes.

  9. Test results, Industrial Solar Technology parabolic trough solar collector

    Energy Technology Data Exchange (ETDEWEB)

    Dudley, V.E. [EG and G MSI, Albuquerque, NM (United States); Evans, L.R.; Matthews, C.W. [Sandia National Labs., Albuquerque, NM (United States)

    1995-11-01

    Sandia National Laboratories and Industrial Solar Technology are cost-sharing development of advanced parabolic trough technology. As part of this effort, several configurations of an IST solar collector were tested to determine the collector efficiency and thermal losses with black chrome and black nickel receiver selective coatings, combined with aluminized film and silver film reflectors, using standard Pyrex{reg_sign} and anti-reflective coated Pyrex{reg_sign} glass receiver envelopes. The development effort has been successful, producing an advanced collector with 77% optical efficiency, using silver-film reflectors, a black nickel receiver coating, and a solgel anti-reflective glass receiver envelope. For each receiver configuration, performance equations were empirically derived relating collector efficiency and thermal losses to the operating temperature. Finally, equations were derived showing collector performance as a function of input insolation value, incident angle, and operating temperature.

  10. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  11. Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

    Institute of Scientific and Technical Information of China (English)

    Hong Jun YUAN; Song Zhe LIAN; Chun Ling CAO; Wen Jie GAO; Xiao Jing XU

    2007-01-01

    The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div(|▽um]p-2▽um). It is proved that the weak solution will be extinct for 1<p≤+1/m and will be positive for p>1+1/m for large t, where m>0.

  12. Fully Nonlinear Parabolic Equations and the Dini Condition

    Institute of Scientific and Technical Information of China (English)

    Xiong ZOU; Ya Zhe CHEN

    2002-01-01

    Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolicequations under the Dini condition, which improve and generalize a result due to Kovats, are obtainedby the use of the approximation lemma.

  13. Spectral Deferred Corrections for Parabolic Partial Differential Equations

    Science.gov (United States)

    2015-06-08

    z) is the amplification factor and the definitions for A-stability, A(α)-stability, and L-stability are identical . In particular, the numerical...1 ) ≤ 1. (4.21) The stability analysis in R3 is identical . As a direct consequence of the definition of stability in (2.18) and L-stability in (2.10...samples on [0, 1], then (5.4) can be restated as f(xj) = n−1 2∑ `=−n−1 2 f̂`e 2πi`tj , j = 0, . . . , n− 1. (5.5) The corresponding trigonometric

  14. A curve flow evolved by a fourth order parabolic equation

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in R2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.

  15. A curve flow evolved by a fourth order parabolic equation

    Institute of Scientific and Technical Information of China (English)

    LIU YanNan; JIAN HuaiYu

    2009-01-01

    We study a fourth order curve flow,which is the gradient flow of a functional describing the shapes of human red blood cells.We prove that for any smooth closed initial curve in R2,the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.

  16. Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods

    Science.gov (United States)

    2014-09-30

    environments in the form of scattering at an elastic interface, oceanic T - waves , and Scholte waves . OBJECTIVES To implement explosive and earthquake...of the the deep ocean where there is no significant sloping bottom. It is believed that ocean bottom roughness scatters the elastic waves up into...Scholte interface waves are excited by seismic sources and have been observed by seismometers at the ocean bottom.[12, 13] Energy from interface waves has

  17. Block Iterative Methods for Elliptic and Parabolic Difference Equations.

    Science.gov (United States)

    1981-09-01

    Wisconsin 53706. (3) University of California, Los Alamos National Laboratory, Los Alamos, New Mexico 87545. *Will also appear as Los Alamos Scientic...Courant, K. Friedrichs, and H. Lewy, Uber die Partiellen Differenzengleichungen der Mathematischen Physik, Math. Ann., 100 (1928), pp. 32-74 = On the

  18. Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis.

    Science.gov (United States)

    Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean

    2011-07-01

    In two space dimensions, the parabolic-parabolic Keller-Segel system shares many properties with the parabolic-elliptic Keller-Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M(c). However, this threshold is not as clear in the parabolic-parabolic case as it is in the parabolic-elliptic case, in which solutions with mass above M(c) always blow up. Here we study forward self-similar solutions of the parabolic-parabolic Keller-Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M(c), which is forbidden in the parabolic-elliptic case.

  19. Acoustic shock wave propagation in a heterogeneous medium: a numerical simulation beyond the parabolic approximation.

    Science.gov (United States)

    Dagrau, Franck; Rénier, Mathieu; Marchiano, Régis; Coulouvrat, François

    2011-07-01

    Numerical simulation of nonlinear acoustics and shock waves in a weakly heterogeneous and lossless medium is considered. The wave equation is formulated so as to separate homogeneous diffraction, heterogeneous effects, and nonlinearities. A numerical method called heterogeneous one-way approximation for resolution of diffraction (HOWARD) is developed, that solves the homogeneous part of the equation in the spectral domain (both in time and space) through a one-way approximation neglecting backscattering. A second-order parabolic approximation is performed but only on the small, heterogeneous part. So the resulting equation is more precise than the usual standard or wide-angle parabolic approximation. It has the same dispersion equation as the exact wave equation for all forward propagating waves, including evanescent waves. Finally, nonlinear terms are treated through an analytical, shock-fitting method. Several validation tests are performed through comparisons with analytical solutions in the linear case and outputs of the standard or wide-angle parabolic approximation in the nonlinear case. Numerical convergence tests and physical analysis are finally performed in the fully heterogeneous and nonlinear case of shock wave focusing through an acoustical lens.

  20. Mineral resource analysis by parabolic fractals

    Institute of Scientific and Technical Information of China (English)

    XIE Shu-yun; YANG Yong-guo; BAO Zheng-yu; KE Xian-zhong; LIU Xiao-long

    2009-01-01

    Elemental concentration distributions in space have been analyzed using different approaches. These analyses are of great significance for the quantitative characterization of various kinds of distribution patterns. Fractal and multi-fiactal methods have been extensively applied to this topic. Traditionally, approximately linear-fractal laws have been regarded as useful tools for characterizing the self-similarities of element concentrations. But, in nature, it is not always easy to fred perfect linear fractal laws. In this paper the parabolic fractal model is used. First a two dimensional multiplicative multi-fractal cascade model is used to study the concentration patterns. The results show the parabolic fractal (PF) properties of the concentrations and the validity of non-linear fractal analysis. By dividing the studied area into four sub-areas it was possible to show that each part follows a non-linear para-bolic fractal law and that the dispersion within each part varies. The ratio of the polynomial coefficients of the fitted parabolic curves can reflect, to some degree, the relative concentration and dispersal distribution patterns. This can provide new insight into the ore-forming potential in space. The parabolic fractal evaluations of ore-forming potential for the four subareas are in good agreement with field investigation work and geochemical mapping results based on analysis of the original data.

  1. Piecewise-Planar Parabolic Reflectarray Antenna

    Science.gov (United States)

    Hodges, Richard; Zawadzki, Mark

    2009-01-01

    The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.

  2. Random perturbations of nonlinear parabolic systems

    CERN Document Server

    Beck, Lisa

    2011-01-01

    Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.

  3. Parabolic flight as a spaceflight analog.

    Science.gov (United States)

    Shelhamer, Mark

    2016-06-15

    Ground-based analog facilities have had wide use in mimicking some of the features of spaceflight in a more-controlled and less-expensive manner. One such analog is parabolic flight, in which an aircraft flies repeated parabolic trajectories that provide short-duration periods of free fall (0 g) alternating with high-g pullout or recovery phases. Parabolic flight is unique in being able to provide true 0 g in a ground-based facility. Accordingly, it lends itself well to the investigation of specific areas of human spaceflight that can benefit from this capability, which predominantly includes neurovestibular effects, but also others such as human factors, locomotion, and medical procedures. Applications to research in artificial gravity and to effects likely to occur in upcoming commercial suborbital flights are also possible. Copyright © 2016 the American Physiological Society.

  4. A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

    Energy Technology Data Exchange (ETDEWEB)

    Addona, Davide, E-mail: d.addona@campus.unimib.it [Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)

    2015-08-15

    We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

  5. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  6. Asymptotical Properties for Parabolic Systems of Neutral Type

    Institute of Scientific and Technical Information of China (English)

    CUI Bao-tong; HAN Mao-an

    2005-01-01

    Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis. The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.

  7. Analytic method for solitary solutions of some partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr

    2007-10-22

    In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.

  8. An Efficient Spectral Approximation for Solving Several Types of Parabolic PDEs with Nonlocal Boundary Conditions

    Directory of Open Access Journals (Sweden)

    E. Tohidi

    2014-01-01

    Full Text Available The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.

  9. 反抛物问题的H(o)lder型稳定性估计%H(o)lder Stability Estimate for an Inverse Parabolic Problem

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    This paper deals with a parabolic system in a multi-dimentional bounded domain Ω Rn with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ωΩ at some time-interval. Our main result is the Holder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations.

  10. The C~α regularity of a class of non-homogeneous ultraparabolic equations

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    We obtain the Cα regularity for weak solutions of a class of non-homogeneous ultra- parabolic equation, with measurable coefficients. The result generalizes our recent Cα regularity results of homogeneous ultraparabolic equations.

  11. Stokes' theorem, volume growth and parabolicity

    CERN Document Server

    Valtorta, Daniele

    2010-01-01

    We present some new Stokes'type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.

  12. CONTINUOUS DEPENDENCE FOR A BACKWARD PARABOLIC PROBLEM

    Institute of Scientific and Technical Information of China (English)

    刘继军

    2003-01-01

    We consider a backward parabolic problem arising in the description of the behavior of the toroidal part of the magenetic field in a dynamo problem. In our backward time problem, the media parameters are spatial distributed and the boundary conditions are of the Robin type. For this ill-posed problem, we prove that the solution depends continuously on the initial-time geometry.

  13. Discontinuous mixed covolume methods for parabolic problems.

    Science.gov (United States)

    Zhu, Ailing; Jiang, Ziwen

    2014-01-01

    We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous H(div) and first-order error estimate in L(2).

  14. Adaptive distributed parameter and input estimation in linear parabolic PDEs

    KAUST Repository

    Mechhoud, Sarra

    2016-01-01

    In this paper, we discuss the on-line estimation of distributed source term, diffusion, and reaction coefficients of a linear parabolic partial differential equation using both distributed and interior-point measurements. First, new sufficient identifiability conditions of the input and the parameter simultaneous estimation are stated. Then, by means of Lyapunov-based design, an adaptive estimator is derived in the infinite-dimensional framework. It consists of a state observer and gradient-based parameter and input adaptation laws. The parameter convergence depends on the plant signal richness assumption, whereas the state convergence is established using a Lyapunov approach. The results of the paper are illustrated by simulation on tokamak plasma heat transport model using simulated data.

  15. The parabolic Anderson model random walk in random potential

    CERN Document Server

    König, Wolfgang

    2016-01-01

    This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.

  16. Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2014-01-01

    Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t  (0≤t≤T,  v(0=v(λ+φ,  0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

  17. Modeling of concentration polarization in a reverse osmosis channel with parabolic crossflow.

    Science.gov (United States)

    Liu, Cui; Morse, Audra; Rainwater, Ken; Song, Lianfa

    2014-01-01

    Concentration polarization in narrow reverse osmosis channels with parabolic crossflow was numerically simulated with finite different equations related to permeate velocity, crossflow velocity, average salt concentration, and wall salt concentration. A significant new theoretical development was the determination of two correction functions, F2 and F3, in the governing equation for average salt concentration. Simulations of concentration polarization under various conditions were then presented to describe the features of the new model as well as discussions about the differences of concentration polarizations of the more realistic parabolic flow with those when plug flow or shear flow was assumed. The situations in which the simpler models based on shear or plug flow can be used were indicated. Concentration polarization was also simulated for various conditions to show the applicability of the model and general features of concentration polarization in a narrow, long reverse osmosis channel.

  18. Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems.

    Science.gov (United States)

    Wang, Zi-Peng; Wu, Huai-Ning; Li, Han-Xiong

    2017-09-01

    In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.

  19. Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

    Directory of Open Access Journals (Sweden)

    Baiyu Wang

    2014-01-01

    Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

  20. Optimal boundary control of a tracking problem for a parabolic distributed system with open-loop control using evolutionary algorithms

    Directory of Open Access Journals (Sweden)

    Russel J Stonier

    2003-08-01

    Full Text Available In this paper we examine the application of evolutionary algorithms to find open-loop control solutions of the optimal control problem arising from the semidiscretisation of a linear parabolic tracking problem with boundary control. The solution is compared with the solutions obtained by methods based upon the variational equations of the Minimum Principle and the finite element method.

  1. The Parabolic Jet Structure in M87 as a Magnetohydrodynamic Nozzle

    CERN Document Server

    Nakamura, Masanori

    2013-01-01

    The structure and dynamics of the M87 jet from sub-milli-arcsec to arcsecond scales are continuously examined. We analysed the VLBA archival data taken at 43 and 86 GHz to measure the size of VLBI cores. Millimeter/sub-mm VLBI cores are considered as innermost jet emissions, which has been originally suggested by Blandford & K\\"onigl. Those components fairly follow an extrapolated parabolic streamline in our previous study so that the jet has a single power-law structure with nearly five orders of magnitude in the distance starting from the vicinity of the supermassive black hole (SMBH), less than 10 Schwarzschild radius ($r_{\\rm s}$). We further inspect the jet parabolic structure as a counterpart of the magnetohydrodynamic (MHD) nozzle in order to identify the property of a bulk acceleration. We interpret that the parabolic jet consists of Poynting-flux dominated flows, powered by large amplitude, nonlinear torsional Alfv\\'en waves. We examine the non-relativistic MHD nozzle equation in a parabolic shap...

  2. Focusing a TM(01) beam with a slightly tilted parabolic mirror.

    Science.gov (United States)

    April, Alexandre; Bilodeau, Pierrick; Piché, Michel

    2011-05-09

    A parabolic mirror illuminated with an incident collimated beam whose axis of propagation does not exactly coincide with the axis of revolution of the mirror shows distortion and strong coma. To understand the behavior of such a focused beam, a detailed description of the electric field in the focal region of a parabolic mirror illuminated with a beam having a nonzero angle of incidence is required. We use the Richards-Wolf vector field equation to investigate the electric energy density distribution of a beam focused with a parabolic mirror. The explicit aberration function of this focused field is provided along with numerically calculated electric energy densities in the focal region for different angles of incidence. The location of the peak intensity, the Strehl ratio and the full-width at half-maximum as a function of the angle of incidence are given and discussed. The results confirm that the focal spot of a strongly focused beam is affected by severe coma, even for very small tilting of the mirror. This analysis provides a clearer understanding of the effect of the angle of incidence on the focusing properties of a parabolic mirror as such a focusing device is of growing interest in microscopy. © 2011 Optical Society of America

  3. Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

    Science.gov (United States)

    Nark, Douglas M.; Watson, Willie R.; Mani, Ramani

    2007-01-01

    A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

  4. Parabolic Anderson model with a finite number of moving catalysts

    CERN Document Server

    Castell, Fabienne; Maillard, Grégory

    2010-01-01

    We consider the parabolic Anderson model (PAM) which is given by the equation $\\partial u/\\partial t = \\kappa\\Delta u + \\xi u$ with $u\\colon\\, \\Z^d\\times [0,\\infty)\\to \\R$, where $\\kappa \\in [0,\\infty)$ is the diffusion constant, $\\Delta$ is the discrete Laplacian, and $\\xi\\colon\\,\\Z^d\\times [0,\\infty)\\to\\R$ is a space-time random environment that drives the equation. The solution of this equation describes the evolution of a ``reactant'' $u$ under the influence of a ``catalyst'' $\\xi$. In the present paper we focus on the case where $\\xi$ is a system of $n$ independent simple random walks each with step rate $2d\\rho$ and starting from the origin. We study the \\emph{annealed} Lyapunov exponents, i.e., the exponential growth rates of the successive moments of $u$ w.r.t.\\ $\\xi$ and show that these exponents, as a function of the diffusion constant $\\kappa$ and the rate constant $\\rho$, behave differently depending on the dimension $d$. In particular, we give a description of the intermittent behavior of the sys...

  5. Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2015-01-07

    In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

  6. Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions

    KAUST Repository

    Ruggeri, Fabrizio

    2016-01-06

    In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.

  7. Parabolic dish collectors - A solar option

    Science.gov (United States)

    Truscello, V. C.

    1981-01-01

    A description is given of several parabolic-dish high temperature solar thermal systems currently undergoing performance trials. A single parabolic dish has the potential for generating 20 to 30 kW of electricity with fluid temperatures from 300 to 1650 C. Each dish is a complete power-producing unit, and may function either independently or as part of a group of linked modules. The two dish designs under consideration are of 11 and 12 meter diameters, yielding receiver operating temperatures of 925 and 815 C, respectively. The receiver designs described include (1) an organic working fluid (toluene) Rankine cycle engine; (2) a Brayton open cycle unit incorporating a hybrid combustion chamber and nozzle and a shaft-coupled permanent magnet alternator; and (3) a modified Stirling cycle device originally designed for automotive use. Also considered are thermal buffer energy storage and thermochemical transport and storage.

  8. Who dares to join a parabolic flight?

    Science.gov (United States)

    Montag, Christian; Zander, Tina; Schneider, Stefan

    2016-12-01

    Parabolic flights represent an important tool in space research to investigate zero gravity on airplanes. Research on these flights often target psychological and biological processes in humans to investigate if and how we can adapt to this unique environment. This research is costly, hard to conduct and clearly heavily relies on humans participating in experiments in this (unnatural) situation. The present study investigated N =66 participants and N =66 matched control persons to study if participants in such experimental flights differ in terms of their personality traits from non-parabonauts. The main finding of this study demonstrates that parabonauts score significantly lower on harm avoidance, a trait closely linked to being anxious. As anxious humans differ from non-anxious humans in their biology, the present observations need to be taken into account when aiming at the generalizability of psychobiological research findings conducted in zero gravity on parabolic flights.

  9. Mechatronic Prototype of Parabolic Solar Tracker.

    Science.gov (United States)

    Morón, Carlos; Díaz, Jorge Pablo; Ferrández, Daniel; Ramos, Mari Paz

    2016-06-15

    In the last 30 years numerous attempts have been made to improve the efficiency of the parabolic collectors in the electric power production, although most of the studies have focused on the industrial production of thermoelectric power. This research focuses on the application of this concentrating solar thermal power in the unexplored field of building construction. To that end, a mechatronic prototype of a hybrid paraboloidal and cylindrical-parabolic tracker based on the Arduido technology has been designed. The prototype is able to measure meteorological data autonomously in order to quantify the energy potential of any location. In this way, it is possible to reliably model real commercial equipment behavior before its deployment in buildings and single family houses.

  10. Mechatronic Prototype of Parabolic Solar Tracker

    Directory of Open Access Journals (Sweden)

    Carlos Morón

    2016-06-01

    Full Text Available In the last 30 years numerous attempts have been made to improve the efficiency of the parabolic collectors in the electric power production, although most of the studies have focused on the industrial production of thermoelectric power. This research focuses on the application of this concentrating solar thermal power in the unexplored field of building construction. To that end, a mechatronic prototype of a hybrid paraboloidal and cylindrical-parabolic tracker based on the Arduido technology has been designed. The prototype is able to measure meteorological data autonomously in order to quantify the energy potential of any location. In this way, it is possible to reliably model real commercial equipment behavior before its deployment in buildings and single family houses.

  11. Dynamical symmetries of semi-linear Schrodinger and diffusion equations

    Energy Technology Data Exchange (ETDEWEB)

    Stoimenov, Stoimen [Laboratoire de Physique des Materiaux , Laboratoire associe au CNRS UMR 7556, Universite Henri Poincare Nancy I, B.P. 239, F-54506 Vandoeuvre les Nancy Cedex (France); Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia (Bulgaria); Henkel, Malte [Laboratoire de Physique des Materiaux, Laboratoire associe au CNRS UMR 7556, Universite Henri Poincare Nancy I, B.P. 239, F-54506 Vandoeuvre les Nancy Cedex (France)]. E-mail: henkel@lpm.u-nancy.fr

    2005-09-12

    Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf{sub 3}){sub C}. We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf{sub 3}){sub C} are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed.

  12. Building a parabolic solar concentrator prototype

    Energy Technology Data Exchange (ETDEWEB)

    Escobar-Romero, J F M; Montiel, S Vazquez y; Granados-AgustIn, F; Rodriguez-Rivera, E; Martinez-Yanez, L [INAOE, Luis Enrique Erro 1, Tonantzintla, Pue., 72840 (Mexico); Cruz-Martinez, V M, E-mail: jfmescobar@yahoo.com [Universidad Tecnologica de la Mixteca, Camino a Acatilma Km 2.5, Huajuapan de Leon, Oax., 69000 (Mexico)

    2011-01-01

    In order to not further degrade the environment, people have been seeking to replace non-renewable natural resources such as fossil fuels by developing technologies that are based on renewable resources. An example of these technologies is solar energy. In this paper, we show the building and test of a solar parabolic concentrator as a prototype for the production of steam that can be coupled to a turbine to generate electricity or a steam engine in any particular industrial process.

  13. Parabolic cylinder functions of large order

    Science.gov (United States)

    Jones, D. S.

    2006-06-01

    The asymptotic behaviour of parabolic cylinder functions of large real order is considered. Various expansions in terms of elementary functions are derived. They hold uniformly for the variable in appropriate parts of the complex plane. Some of the expansions are doubly asymptotic with respect to the order and the complex variable which is an advantage for computational purposes. Error bounds are determined for the truncated versions of the asymptotic series.

  14. INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES

    Institute of Scientific and Technical Information of China (English)

    Liu Zhenhai; I.Szántó

    2011-01-01

    This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality.The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained.

  15. Study on a Cross Diffusion Parabolic System

    Institute of Scientific and Technical Information of China (English)

    Li Chen; Ling Hsiao; Gerald Warnecke

    2007-01-01

    This paper considers a kind of strongly coupled cross diffusion parabolic system, which can be used as the multi-dimensional Lyumkis energy transport model in semiconductor science. The global existence and large time behavior are obtained for smooth solution to the initial boundary value problem. When the initial data are a small perturbation of an isothermal stationary solution, the smooth solution of the problem under the insulating boundary condition, converges to that stationary solution exponentially fast as time goes to infinity.

  16. Refined Error Estimates for the Riccati Equation with Applications to the Angular Teukolsky Equation

    CERN Document Server

    Finster, Felix

    2013-01-01

    We derive refined rigorous error estimates for approximate solutions of Sturm-Liouville and Riccati equations with real or complex potentials. The approximate solutions include WKB approximations, Airy and parabolic cylinder functions, and certain Bessel functions. Our estimates are applied to solutions of the angular Teukolsky equation with a complex aspherical parameter in a rotating black hole Kerr geometry.

  17. Parabolic resection for mitral valve repair.

    Science.gov (United States)

    Drake, Daniel H; Drake, Charles G; Recchia, Dino

    2010-02-01

    Parabolic resection, named for the shape of the cut edges of the excised tissue, expands on a common 'trick' used by experienced mitral surgeons to preserve tissue and increase the probability of successful repair. Our objective was to describe and clinically analyze this simple modification of conventional resection. Thirty-six patients with mitral regurgitation underwent valve repair using parabolic resection in combination with other techniques. Institution specific mitral data, Society of Thoracic Surgeons data and preoperative, post-cardiopulmonary bypass (PCPB) and postoperative echocardiography data were collected and analyzed. Preoperative echocardiography demonstrated mitral regurgitation ranging from moderate to severe. PCPB transesophageal echocardiography demonstrated no regurgitation or mild regurgitation in all patients. Thirty-day surgical mortality was 2.8%. Serial echocardiograms demonstrated excellent repair stability. One patient (2.9%) with rheumatic disease progressed to moderate regurgitation 33 months following surgery. Echocardiography on all others demonstrated no or mild regurgitation at a mean follow-up of 22.8+/-12.8 months. No patient required mitral reintervention. Longitudinal analysis demonstrated 80% freedom from cardiac death, reintervention and greater than moderate regurgitation at four years following repair. Parabolic resection is a simple technique that can be very useful during complex mitral reconstruction. Early and intermediate echocardiographic studies demonstrate excellent results.

  18. Simulation of parabolic reflectors for ultraviolet phototherapy

    Science.gov (United States)

    Grimes, David Robert

    2016-08-01

    Ultraviolet (UVR) phototherapy is widely used to treat an array of skin conditions, including psoriasis, eczema and vitiligo. For such interventions, a quantified dose is vital if the treatment is to be both biologically effective and to avoid the detrimental effects of over-dosing. As dose is absorbed at surface level, the orientation of patient site with respect to the UVR lamps modulates effective dose. Previous investigations have modelled this behaviour, and examined the impact of shaped anodized aluminium reflectors typically placed around lamps in phototherapy cabins. These mirrors are effective but tend to yield complex patterns of reflection around the cabin which can result in substantial dose inhomogeneity. There has been some speculation over whether using the reflective property of parabolic mirrors might improve dose delivery or homogeneity through the treatment cabin. In this work, the effects of parabolic mirrors are simulated and compared with standard shaped mirrors. Simulation results strongly suggest that parabolic reflectors reduce total irradiance relative to standard shaped reflectors, and have a negligible impact on dose homogeneity.

  19. Simulation of parabolic reflectors for ultraviolet phototherapy.

    Science.gov (United States)

    Robert Grimes, David

    2016-08-21

    Ultraviolet (UVR) phototherapy is widely used to treat an array of skin conditions, including psoriasis, eczema and vitiligo. For such interventions, a quantified dose is vital if the treatment is to be both biologically effective and to avoid the detrimental effects of over-dosing. As dose is absorbed at surface level, the orientation of patient site with respect to the UVR lamps modulates effective dose. Previous investigations have modelled this behaviour, and examined the impact of shaped anodized aluminium reflectors typically placed around lamps in phototherapy cabins. These mirrors are effective but tend to yield complex patterns of reflection around the cabin which can result in substantial dose inhomogeneity. There has been some speculation over whether using the reflective property of parabolic mirrors might improve dose delivery or homogeneity through the treatment cabin. In this work, the effects of parabolic mirrors are simulated and compared with standard shaped mirrors. Simulation results strongly suggest that parabolic reflectors reduce total irradiance relative to standard shaped reflectors, and have a negligible impact on dose homogeneity.

  20. Nonlocal Optical Spatial Soliton with a Non-parabolic Symmetry and Real-valued Convolution Response Kernel

    Institute of Scientific and Technical Information of China (English)

    LI Ke-Ping; YU Chao-Fan; GAO Zi-You; LIANG Guo-Dong; YU Xiao-Min

    2008-01-01

    Based on the picture of nonlinear and non-parabolic symmetry response, I.e., △n2( I) ≈ p(αo -α1x- α2x2), we propose a model for the transversal beam intensity distribution of the nonlocal spatial soliton. In this model, as a convolution response with non-parabolic symmetry, △n2( I) ≈ p(b0+b1 f - b2 f2 with b2/b1 > 0 is assumed. Furthermore, instead of the wave function Ψ, the high-order nonlinear equation for the beam intensity distribution f has been derived and the bell-shaped soliton solution with the envelope form has been obtained. The results demonstrate that, since the existence of the terms of non-parabolic response, the nonlocal spatial soliton has the bistable state solution. If thefrequency shift of wave number β satisfies 0 0 has been demonstrated.

  1. Distributed Proportional-spatial Derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach.

    Science.gov (United States)

    Wang, Jun-Wei; Wu, Huai-Ning; Li, Han-Xiong

    2012-06-01

    In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.

  2. Femtosecond parabolic pulse shaping in normally dispersive optical fibers.

    Science.gov (United States)

    Sukhoivanov, Igor A; Iakushev, Sergii O; Shulika, Oleksiy V; Díez, Antonio; Andrés, Miguel

    2013-07-29

    Formation of parabolic pulses at femtosecond time scale by means of passive nonlinear reshaping in normally dispersive optical fibers is analyzed. Two approaches are examined and compared: the parabolic waveform formation in transient propagation regime and parabolic waveform formation in the steady-state propagation regime. It is found that both approaches could produce parabolic pulses as short as few hundred femtoseconds applying commercially available fibers, specially designed all-normal dispersion photonic crystal fiber and modern femtosecond lasers for pumping. The ranges of parameters providing parabolic pulse formation at the femtosecond time scale are found depending on the initial pulse duration, chirp and energy. Applicability of different fibers for femtosecond pulse shaping is analyzed. Recommendation for shortest parabolic pulse formation is made based on the analysis presented.

  3. Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory

    Directory of Open Access Journals (Sweden)

    M. Jakomin

    2011-01-01

    Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.

  4. Thermal performance of functionally graded parabolic annular fins having constant weight

    Energy Technology Data Exchange (ETDEWEB)

    Gaba, Vivek Kumar; Tiwari, Anil Kumar; Bhowmick, Shubhankar [National Institute of Technology Raipur, Raipur (India)

    2014-10-15

    The proposed work reports the performance of parabolic annular fins of constant weight made of functionally graded materials. The work involves computation of temperature gradient, efficiency and effectiveness of such fins and compares the performances for different functionally graded parabolic fin profiles obtained by varying grading parameters and profile parameters respectively keeping the weight of the fins constant. The functional grading of thermal conductivity is based on a power function of radial co-ordinate which consists of parameters, namely grading parameters, varying which different grading combinations are studied. A general second order ordinary differential equation has been derived for all the profiles and material grading. The efficiency and effectiveness of the annular fins of different profile and grading combinations have been calculated and plotted and the results reveal the dependence of fin performance on profile and grading parameter.

  5. Linear Parabolic Maps on the Torus

    CERN Document Server

    Zyczkowski, K; Zyczkowski, Karol; Nishikawa, Takashi

    1999-01-01

    We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of the maximal invariant set, and in a generic case we prove the sensitive dependence on the initial conditions. We study the decay of correlations and the diffusion in the corresponding system on the plane. We also demonstrate how the rationality of the real numbers defining the map influences the dynamical properties of the system.

  6. Surface roughness estimation of a parabolic reflector

    CERN Document Server

    Casco, Nicolás A

    2010-01-01

    Random surface deviations in a reflector antenna reduce the aperture efficiency. This communication presents a method for estimating the mean surface deviation of a parabolic reflector from a set of measured points. The proposed method takes into account systematic measurement errors, such as the offset between the origin of reference frame and the vertex of the surface, and the misalignment between the surface rotation axis and the measurement axis. The results will be applied to perform corrections to the surface of one of the 30 m diameter radiotelescopes at the Instituto Argentino de Radioastronom\\'ia (IAR).

  7. Parabolic dunes in north-eastern Brazil

    CERN Document Server

    Duran, O; Bezerra, L J C; Herrmann, H J; Maia, L P

    2007-01-01

    In this work we present measurements of vegetation cover over parabolic dunes with different degree of activation along the north-eastern Brazilian coast. We are able to extend the local values of the vegetation cover density to the whole dune by correlating measurements with the gray-scale levels of a high resolution satellite image of the dune field. The empirical vegetation distribution is finally used to validate the results of a recent continuous model of dune motion coupling sand erosion and vegetation growth.

  8. Alignment method for parabolic trough solar concentrators

    Science.gov (United States)

    Diver, Richard B [Albuquerque, NM

    2010-02-23

    A Theoretical Overlay Photographic (TOP) alignment method uses the overlay of a theoretical projected image of a perfectly aligned concentrator on a photographic image of the concentrator to align the mirror facets of a parabolic trough solar concentrator. The alignment method is practical and straightforward, and inherently aligns the mirror facets to the receiver. When integrated with clinometer measurements for which gravity and mechanical drag effects have been accounted for and which are made in a manner and location consistent with the alignment method, all of the mirrors on a common drive can be aligned and optimized for any concentrator orientation.

  9. Asymptotic behaviour for a diffusion equation governed by nonlocal interactions

    CERN Document Server

    Ovono, Armel Andami

    2010-01-01

    In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.

  10. Focusing parabolic guide for very small samples

    Energy Technology Data Exchange (ETDEWEB)

    Hils, T.; Boeni, P.; Stahn, J

    2004-07-15

    Modern materials can often only be grown in small quantities. Therefore, neutron-scattering experiments are difficult to perform due to the low signal. In order to increase the flux at the sample position, we have developed the concept of a small focusing guide tube with parabolically shaped walls that are coated with supermirror m=3. The major advantage of parabolic focusing is that the flux maximum occurs not at the exit of the tube. It occurs at the focal point that can be several centimeters away from the exit of the tube. We show that an intensity gain of 6 can easily be obtained. Simulations using the software package McStas demonstrate that gain factors up to more than 50 can be realised on a spot size of approximately 1.2 mm diameter. For PGAA we expect flux gains of up to three orders of magnitude if multiplexing is used. We show that elliptic ballistic guides lead to flux gains of more than 6.

  11. Focusing parabolic guide for very small samples

    Science.gov (United States)

    Hils, T.; Boeni, P.; Stahn, J.

    2004-07-01

    Modern materials can often only be grown in small quantities. Therefore, neutron-scattering experiments are difficult to perform due to the low signal. In order to increase the flux at the sample position, we have developed the concept of a small focusing guide tube with parabolically shaped walls that are coated with supermirror m=3. The major advantage of parabolic focusing is that the flux maximum occurs not at the exit of the tube. It occurs at the focal point that can be several centimeters away from the exit of the tube. We show that an intensity gain of 6 can easily be obtained. Simulations using the software package McStas demonstrate that gain factors up to more than 50 can be realised on a spot size of approximately 1.2 mm diameter. For PGAA we expect flux gains of up to three orders of magnitude if multiplexing is used. We show that elliptic ballistic guides lead to flux gains of more than 6.

  12. STABILITY OF A PARABOLIC FIXED POINT OF REVERSIBLE MAPPINGS

    Institute of Scientific and Technical Information of China (English)

    LIUBIN; YOUJIANGONG

    1994-01-01

    KAM theorem of reversible system is used to provide a sufficient condition which guarantees the stability of a parabolic fixed point of reversible mappings, The main idea is to discuss when the parabolic fixed point is surrounded by closed invariant carves and thus exhibits stable behaviour.

  13. Manipulation of dielectric particles with nondiffracting parabolic beams.

    Science.gov (United States)

    Ortiz-Ambriz, Antonio; Gutiérrez-Vega, Julio C; Petrov, Dmitri

    2014-12-01

    The trapping and manipulation of microscopic particles embedded in the structure of nondiffracting parabolic beams is reported. The particles acquire orbital angular momentum and exhibit an open trajectory following the parabolic fringes of the beam. We observe an asymmetry in the terminal velocity of the particles caused by the counteracting gradient and scattering forces.

  14. Surface plasmon polariton beam focusing with parabolic nanoparticle chains

    DEFF Research Database (Denmark)

    Radko, Ilya P.; Bozhevolnyi, Sergey I.; Evlyukhin, Andrey B.

    2007-01-01

    We report on the focusing of surface plasmon polariton (SPP) beams with parabolic chains of gold nanoparticles fabricated on thin gold films. SPP focusing with different parabolic chains is investigated in the wavelength range of 700–860 nm, both experimentally and theoretically. Mapping of SPP...

  15. Polaron Energy and Effective Mass in Parabolic Quantum Wells

    Institute of Scientific and Technical Information of China (English)

    WANG Zhi-Ping; LIANG Xi-Xia

    2005-01-01

    @@ The energy and effective mass of a polaron in a parabolic quantum well are studied theoretically by using LLP-like transformations and a variational approach. Numerical results are presented for the polaron energy and effective mass in the GaAs/Al0.3Ga0.7As parabolic quantum well. The results show that the energy and the effective mass of the polaron both have their maxima in the finite parabolic quantum well but decrease monotonously in the infinite parabolic quantum well with the increasing well width. It is verified that the bulk longitudinal optical phonon mode approximation is an adequate formulation for the electron-phonon coupling in parabolic quantum well structures.

  16. Optical, Energetic and Exergetic Analyses of Parabolic Trough Collectors

    Institute of Scientific and Technical Information of China (English)

    (O)ZT(U)RK Murat; (C)(I)(C)EK BEZ(I)R Nalan; (O)ZEK Nuri

    2007-01-01

    Parabolic trough collectors generate thermal energy from solar energy. Especially, they are very convenient for applications in high temperature solar power systems. To determine the design parameters, parabolic trough collectors must be analysed with optical analysis. In addition, thermodynamics (energy and exergy) analysis in the development of an energy efficient system must be achieved. Solar radiation passes through Earth's atmosphere until it reaches on Earth's surface and is focused from the parabolic trough collector to the tube receiver with a transparent insulated envelope. All of them constitute a complex mechanism. We investigate the geometry of parabolic trough reflector and characteristics of solar radiation to the reflecting surface through Earth's atmosphere, and calculate the collecting total energy in the receiver. The parabolic trough collector,of which design parameters are given, is analysed in regard to the energy and exergy analysis considering the meteorological specification in May, June, July and August in Isparta/Turkey, and the results are presented.

  17. A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems

    Energy Technology Data Exchange (ETDEWEB)

    Kamynin, L I; Khimchenko, B N

    2001-08-31

    We consider two classes of second-order parabolic matrix-vector systems (with solutions u element of M{sub mx1}, m{>=}2) that can be reduced to a single second-order parabolic equation for a scalar function v=, where p element of M{sub mx1} is a fixed stochastic constant vector. We consider the first boundary-value problem for a scalar second-order parabolic equation (with unbounded coefficients) in a domain unbounded with respect to x under the assumption of strong absorption at infinity. We obtain an a priori estimate for solutions of the first boundary-value problem in the generalized Tikhonov-Taecklind classes. (The problem under investigation has at most one solution in these classes.)

  18. The Effect of Boundary Support and Reflector Dimensions on Inflatable Parabolic Antenna Performance

    Science.gov (United States)

    Coleman, Michael J.; Baginski, Frank; Romanofsky, Robert R.

    2011-01-01

    For parabolic antennas with sufficient surface accuracy, more power can be radiated with a larger aperture size. This paper explores the performance of antennas of various size and reflector depth. The particular focus is on a large inflatable elastic antenna reflector that is supported about its perimeter by a set of elastic tendons and is subjected to a constant hydrostatic pressure. The surface accuracy of the antenna is measured by an RMS calculation, while the reflector phase error component of the efficiency is determined by computing the power density at boresight. In the analysis, the calculation of antenna efficiency is not based on the Ruze Equation. Hence, no assumption regarding the distribution of the reflector surface distortions is presumed. The reflector surface is modeled as an isotropic elastic membrane using a linear stress-strain constitutive relation. Three types of antenna reflector construction are considered: one molded to an ideal parabolic form and two different flat panel design patterns. The flat panel surfaces are constructed by seaming together panels in a manner that the desired parabolic shape is approximately attained after pressurization. Numerical solutions of the model problem are calculated under a variety of conditions in order to estimate the accuracy and efficiency of these antenna systems. In the case of the flat panel constructions, several different cutting patterns are analyzed in order to determine an optimal cutting strategy.

  19. Smoothing and Decay Estimates for Nonlinear Diffusion Equations Equations of Porous Medium Type

    CERN Document Server

    Vázquez, Juan Luis

    2006-01-01

    This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porou

  20. Thermo-electronic solar power conversion with a parabolic concentrator

    Science.gov (United States)

    Olukunle, Olawole C.; De, Dilip K.

    2016-02-01

    We consider the energy dynamics of the power generation from the sun when the solar energy is concentrated on to the emitter of a thermo-electronic converter with the help of a parabolic mirror. We use the modified Richardson-Dushman equation. The emitter cross section is assumed to be exactly equal to the focused area at a height h from the base of the mirror to prevent loss of efficiency. We report the variation of output power with solar insolation, height h, reflectivity of the mirror, and anode temperature, initially assuming that there is no space charge effect. Our methodology allows us to predict the temperature at which the anode must be cooled in order to prevent loss of efficiency of power conversion. Novel ways of tackling the space charge problem have been discussed. The space charge effect is modeled through the introduction of a parameter f (0 solar insolation, height h, apart from radii R of the concentrator aperture and emitter, and the collector material properties. We have also considered solar thermos electronic power conversion by using single atom-layer graphene as an emitter.

  1. Adaptive Stabilization for ODE Systems Coupled with Parabolic PDES

    Institute of Scientific and Technical Information of China (English)

    LI Jian; LIU Yungang

    2016-01-01

    This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs.The presence of the uncertainties/unknonws and the coupling between the sub-systems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design.Motivated by the related literature,an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one,from which the control design becomes much convenient.It is worthwhile pointing out that,since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded,the desirable kernel functions are more difficult to derive than those of the closely related literature.Then,by Lyapunov method and a dynamics compensated technique,an adaptive stabilizing controller is successfully constructed,which guarantees that all the closed-loop system states are bounded while the original system states converging to zero.Finally,a simulation example is provided to validate the proposed method.

  2. Experimental Investigation of Pressure-volume-Temperature Mass Gauging Method Under Microgravity Condition by Parabolic Flight

    Science.gov (United States)

    Seo, Mansu; Park, Hana; Yoo, DonGyu; Jung, Youngsuk; Jeong, Sangkwon

    Gauging the volume or mass of liquid propellant of a rocket vehicle in space is an important issue for its economic feasibility and optimized design of loading mass. Pressure-volume-temperature (PVT) gauging method is one of the most suitable measuring techniques in space due to its simplicity and reliability. This paper presents unique experimental results and analyses of PVT gauging method using liquid nitrogen under microgravity condition by parabolic flight. A vacuum-insulated and cylindrical-shaped liquid nitrogen storage tank with 9.2 L volume is manufactured by observing regulation of parabolic flight. PVT gauging experiments are conducted under low liquid fraction condition from 26% to 32%. Pressure, temperature, and the injected helium mass into the storage tank are measured to obtain the ullage volume by gas state equation. Liquid volume is finally derived by the measured ullage volume and the known total tank volume. Two sets of parabolic flights are conducted and each set is composed of approximately 10 parabolic flights. In the first set of flights, the short initial waiting time (3 ∼ 5 seconds) cannot achieve sufficient thermal equilibrium condition at the beginning. It causes inaccurate gauging results due to insufficient information of the initial helium partial pressure in the tank. The helium injection after 12 second waiting time at microgravity condition with high mass flow rate in the second set of flights achieves successful initial thermal equilibrium states and accurate measurement results of initial helium partial pressure. Liquid volume measurement errors in the second set are within 11%.

  3. Parabolic refined invariants and Macdonald polynomials

    CERN Document Server

    Chuang, Wu-yen; Donagi, Ron; Pantev, Tony

    2013-01-01

    A string theoretic derivation is given for the conjecture of Hausel, Letellier, and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with G. Pan. Haiman's geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.

  4. Antireflection Pyrex envelopes for parabolic solar collectors

    Science.gov (United States)

    McCollister, H. L.; Pettit, R. B.

    1983-11-01

    Antireflective (AR) coatings, applied to the glass envelopes used in parabolic trough solar collectors around the receiver tube in order to reduce thermal losses, can increase solar transmittance by 7 percent. An AR surface has been formed on Pyrex by first heat treating the glass to cause a compositional phase separation, removing a surface layer after heat treatment through the use of a preetching solution, and finally etching in a solution that contains hydrofluorosilic and ammonium bifluoride acids. AR-coated samples with solar transmittance values of more than 0.97, by comparison to an untreated sample value of 0.91, have been obtained for the 560-630 C range of heat treatment temperatures. Optimum values have also been determined for the other processing parameters.

  5. Photon-Atom Coupling with Parabolic Mirrors

    CERN Document Server

    Sondermann, Markus

    2014-01-01

    Efficient coupling of light to single atomic systems has gained considerable attention over the past decades. This development is driven by the continuous growth of quantum technologies. The efficient coupling of light and matter is an enabling technology for quantum information processing and quantum communication. And indeed, in recent years much progress has been made in this direction. But applications aside, the interaction of photons and atoms is a fundamental physics problem. There are various possibilities for making this interaction more efficient, among them the apparently 'natural' attempt of mode-matching the light field to the free-space emission pattern of the atomic system of interest. Here we will describe the necessary steps of implementing this mode-matching with the ultimate aim of reaching unit coupling efficiency. We describe the use of deep parabolic mirrors as the central optical element of a free-space coupling scheme, covering the preparation of suitable modes of the field incident on...

  6. Analysis of the Quality of Parabolic Flight

    Science.gov (United States)

    Lambot, Thomas; Ord, Stephan F.

    2016-01-01

    Parabolic flight allows researchers to conduct several micro-gravity experiments, each with up to 20 seconds of micro-gravity, in the course of a single day. However, the quality of the flight environment can vary greatly over the course of a single parabola, thus affecting the experimental results. Researchers therefore require knowledge of the actual flight environment as a function of time. The NASA Flight Opportunities program (FO) has reviewed the acceleration data for over 400 parabolas and investigated the level of micro-gravity quality. It was discovered that a typical parabola can be segmented into multiple phases with different qualities and durations. The knowledge of the microgravity characteristics within the parabola will prove useful when planning an experiment.

  7. Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity.

    Science.gov (United States)

    Chen, Shihua; Yi, Lin; Guo, Dong-Sheng; Lu, Peixiang

    2005-07-01

    Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.

  8. Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization

    CERN Document Server

    Deolmi, Giulia

    2011-01-01

    This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a projected damped Gauss-Newton, in the second one it is ill-posed and an adaptive parametrization with time localization will be adopted to regularize it. To solve the optimization loop a model reduction technique (Proper Orthogonal Decomposition) is used.

  9. Numerical computation of pyramidal quantum dots with band non-parabolicity

    Science.gov (United States)

    Gong, Liang; Shu, Yong-chun; Xu, Jing-jun; Wang, Zhan-guo

    2013-09-01

    This paper presents an effective and feasible eigen-energy scanning method to solve polynomial matrix eigenvalues introduced by 3D quantum dots problem with band non-parabolicity. The pyramid-shaped quantum dot is placed in a computational box with uniform mesh in Cartesian coordinates. Its corresponding Schrödinger equation is discretized by the finite difference method. The interface conditions are incorporated into the discretization scheme without explicitly enforcing them. By comparing the eigenvalues from isolated quantum dots and a vertically aligned regular array of them, we investigate the coupling effect for variable distances between the quantum dots and different size.

  10. A scaling limit theorem for the parabolic Anderson model with exponential potential

    CERN Document Server

    Lacoin, Hubert

    2010-01-01

    The parabolic Anderson problem is the Cauchy problem for the heat equation with random potential and localized initial condition. In this paper we consider potentials which are constant in time and independent exponentially distributed in space. We study the growth rate of the total mass of the solution in terms of weak and almost sure limit theorems, and the spatial spread of the mass in terms of a scaling limit theorem. The latter result shows that in this case, just like in the case of heavy tailed potentials, the mass gets trapped in a single relevant island with high probability.

  11. A MONOTONE DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Igor Boglaev; Matthew Hardy

    2008-01-01

    This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.

  12. Tracking local control of a parabolic trough collector; Control local de seguimiento cilindro parabolico ACE20

    Energy Technology Data Exchange (ETDEWEB)

    Ajona, J.I.; Alberdi, J.; Gamero, E.; Blanco, J.

    1992-07-01

    In the local control, the sun position related to the trough collector is measured by two photo-resistors. The provided electronic signal is then compared with reference levels in order to get a set of B logical signals which form a byte. This byte and the commands issued by a programmable controller are connected to the inputs of o P.R.O.M. memory which is programmed with the logical equations of the control system. The memory output lines give the control command of the parabolic trough collector motor. (Author)

  13. A New Algorithm for System of Integral Equations

    Directory of Open Access Journals (Sweden)

    Abdujabar Rasulov

    2014-01-01

    Full Text Available We develop a new algorithm to solve the system of integral equations. In this new method no need to use matrix weights. Beacause of it, we reduce computational complexity considerable. Using the new algorithm it is also possible to solve an initial boundary value problem for system of parabolic equations. To verify the efficiency, the results of computational experiments are given.

  14. Heat polynomial analogs for higher order evolution equations

    Directory of Open Access Journals (Sweden)

    G. N. Hile

    2001-05-01

    Full Text Available Polynomial solutions analogous to the heat polynomials are demonstrated for higher order linear homogeneous evolution equations with coefficients depending on the time variable. Further parallels with the heat polynomials are established when the equation is parabolic with constant coefficients and only highest order terms.

  15. Euler-Chebyshev methods for integro-differential equations

    NARCIS (Netherlands)

    Houwen, P.J. van der; Sommeijer, B.P.

    1996-01-01

    We construct and analyse explicit methods for solving initial value problems for systems of differential equations with expensive righthand side functions whose Jacobian has its stiff eigenvalues along the negative axis. Such equations arise after spatial discretization of parabolic integro-differen

  16. Two new designs of parabolic solar collectors

    Directory of Open Access Journals (Sweden)

    Karimi Sadaghiyani Omid

    2014-01-01

    Full Text Available In this work, two new compound parabolic trough and dish solar collectors are presented with their working principles. First, the curves of mirrors are defined and the mathematical formulation as one analytical method is used to trace the sun rays and recognize the focus point. As a result of the ray tracing, the distribution of heat flux around the inner wall can be reached. Next, the heat fluxes are calculated versus several absorption coefficients. These heat flux distributions around absorber tube are functions of angle in polar coordinate system. Considering, the achieved heat flux distribution are used as a thermal boundary condition. After that, Finite Volume Methods (FVM are applied for simulation of absorber tube. The validation of solving method is done by comparing with Dudley's results at Sandia National Research Laboratory. Also, in order to have a good comparison between LS-2 and two new designed collectors, some of their parameters are considered equal with together. These parameters are consist of: the aperture area, the measures of tube geometry, the thermal properties of absorber tube, the working fluid, the solar radiation intensity and the mass flow rate of LS-2 collector are applied for simulation of the new presented collectors. After the validation of the used numerical models, this method is applied to simulation of the new designed models. Finally, the outlet results of new designed collector are compared with LS-2 classic collector. Obviously, the obtained results from the comparison show the improving of the new designed parabolic collectors efficiency. In the best case-study, the improving of efficiency are about 10% and 20% for linear and convoluted models respectively.

  17. Sener Parabolic trough Collector Design and Testing

    Energy Technology Data Exchange (ETDEWEB)

    Castaneda, N.; Vazquez, J.; Domingo, M.

    2006-07-01

    Parabolic trough technology is nowadays the most extended solar system for electricity production or steam generation for industrial processes. It is basically composed of a collector field which converts solar irradiation into thermal energy- and a conventional thermal-toelectric conversion Rankine cycle. In these plants, a storage system can be implemented in order to increase plant production. Collector field represents more than half the total plant cost. Therefore, SENER has made an effort to improve current state of the art of parabolic trough collector (PTC from now on) design in order to reduce plant costs. Main characteristic of SENER design lies on the use of a torque tube as the central body of the collector. This tube is made of steel sheet, with a thickness depending on wind load requirements on the collector. This concept is very cost-effective, since the man-power needed to manufacture the tube has been minimized. Continuous cylindrical shape of the torque tube provides a high torsional stiffness, which is one of the main parameters affecting collector optical efficiency. Cantilever arms connect the mirrors to the central torque tube. These components are usually made of welded tube profiles. In SENER's new design, these cantilever arms are made using metal sheet stamping techniques (SENER patent), thus reducing manufacturing and mounting costs. SENER PTC module (called SENERTROUGH) is 12 meters long and has an aperture width of 5,76 m. HCE and curved mirrors existing in the market - as well as new products from different manufacturers - can be easily attached to collector structure. Two prototype modules of SENERTROUGH have been mounted and tested at the CIEMAT-PSA facilities. Several performance tests were performed in order to assure the validity of the concept. (Author)

  18. A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems

    Science.gov (United States)

    Zheng, Zheming; Simeon, Bernd; Petzold, Linda

    2008-05-01

    A fully explicit, stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations (PDEs) is presented. Writing the semi-discretized equations as a differential-algebraic equation (DAE) system where the interface continuity constraints between subdomains are enforced by Lagrange multipliers, the method uses the Runge-Kutta-Chebyshev projection scheme to integrate the DAE explicitly and to enforce the constraints by a projection. With mass lumping techniques and node-to-node matching grids, the method is fully explicit without solving any linear system. A stability analysis is presented to show the extended stability property of the method. The method is straightforward to implement and to parallelize. Numerical results demonstrate that it has excellent performance.

  19. On a nonhomogeneous Burgers' equation

    Institute of Scientific and Technical Information of China (English)

    DING; Xiaqi(

    2001-01-01

    [1]Hopf, E., The partial differential equation ut + uux = μuxx, Comm. Pure Appl. Math., 1950, 3: 201-230.[2]Ding, X. Q. , Luo, P. Z. , Generalized expansions in Hilbert space, Acta Mathematica Scientia, 1999, 19(3): 241 250.[3]Titchmarsh, E., Introduction to the Theory of Fourier Integrals, 2nd ed., Oxford: Oxford University Press, 1948.[4]Ladyzhenskaya, O. A., Solonnikov, V. A., Ural' ceva, N. N., Linear and Quasilinear Equations of Parabolic Type,Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, 1968.

  20. Parabolic features and the erosion rate on Venus

    Science.gov (United States)

    Strom, Robert G.

    1993-01-01

    The impact cratering record on Venus consists of 919 craters covering 98 percent of the surface. These craters are remarkably well preserved, and most show pristine structures including fresh ejecta blankets. Only 35 craters (3.8 percent) have had their ejecta blankets embayed by lava and most of these occur in the Atla-Beta Regio region; an area thought to be recently active. parabolic features are associated with 66 of the 919 craters. These craters range in size from 6 to 105 km diameter. The parabolic features are thought to be the result of the deposition of fine-grained ejecta by winds in the dense venusian atmosphere. The deposits cover about 9 percent of the surface and none appear to be embayed by younger volcanic materials. However, there appears to be a paucity of these deposits in the Atla-Beta Regio region, and this may be due to the more recent volcanism in this area of Venus. Since parabolic features are probably fine-grain, wind-deposited ejecta, then all impact craters on Venus probably had these deposits at some time in the past. The older deposits have probably been either eroded or buried by eolian processes. Therefore, the present population of these features is probably associated with the most recent impact craters on the planet. Furthermore, the size/frequency distribution of craters with parabolic features is virtually identical to that of the total crater population. This suggests that there has been little loss of small parabolic features compared to large ones, otherwise there should be a significant and systematic paucity of craters with parabolic features with decreasing size compared to the total crater population. Whatever is erasing the parabolic features apparently does so uniformly regardless of the areal extent of the deposit. The lifetime of parabolic features and the eolian erosion rate on Venus can be estimated from the average age of the surface and the present population of parabolic features.