WorldWideScience

Sample records for boundary value problems

  1. Non-normal Hasemann Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    We will discuss the non-normal Hasemann boundary value problem:we may find these results are coincided with those of normal Hasemann boundary value problem and non normal Riemann boundary value problem.

  2. Boundary value problems and partial differential equations

    CERN Document Server

    Powers, David L

    2005-01-01

    Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples

  3. Boundary Value Problems Arising in Kalman Filtering

    Directory of Open Access Journals (Sweden)

    Sinem Ertürk

    2009-01-01

    Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.

  4. Boundary Value Problems Arising in Kalman Filtering

    Directory of Open Access Journals (Sweden)

    Bashirov Agamirza

    2008-01-01

    Full Text Available The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.

  5. Fourier analysis and boundary value problems

    CERN Document Server

    Gonzalez-Velasco, Enrique A

    1996-01-01

    Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...

  6. Semigroups, boundary value problems and Markov processes

    CERN Document Server

    Taira, Kazuaki

    2014-01-01

    A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes ...

  7. Boundary value problems and medical imaging

    International Nuclear Information System (INIS)

    The application of appropriate transform pairs, such as the Fourier, the Laplace, the sine, the cosine and the Mellin transforms, provides the most well known method for constructing analytical solutions to a large class of physically significant boundary value problems. However, this method has several limitations. In particular, it requires the given PDE, domain and boundary conditions to be separable, and also may not be applicable if the given boundary value problem is non-self-adjoint. Furthermore, it expresses the solution as either an integral or an infinite series, neither of which are uniformly convergent on the boundary of the domain (for nonvanishing boundary conditions), which renders such expressions unsuitable for numerical computations. Here, we review a method recently introduced by the first author which can be applied to certain nonseparable and non-self-adjoint problems. Furthermore, this method expresses the solution as an integral in the complex plane which is uniformly convergent on the boundary of the domain. This method, which also suggests new numerical techniques, is illustrated for both evolution and elliptic PDEs. Athough this method was first applied to certain nonlinear PDEs called integrable and was originally formulated in terms of the so-called Lax pairs, it can actually be applied to linear PDEs without the need to analyse the associated Lax pair. The existence of Lax pairs is used here in order to motivate a related development, namely the emergence of a novel formalism for analysing certain inverse problems arising in medical imaging. Examples include PET and SPECT

  8. Unique solution to periodic boundary value problems

    Directory of Open Access Journals (Sweden)

    Yong Sun

    1991-01-01

    Full Text Available Existence of unique solution to periodic boundary value problems of differential equations with continuous or discontinuous right-hand side is considered by utilizing the method of lower and upper solutions and the monotone properties of the operator. This is subject to discussion in the present paper.

  9. Topological invariants in nonlinear boundary value problems

    Energy Technology Data Exchange (ETDEWEB)

    Vinagre, Sandra [Departamento de Matematica, Universidade de Evora, Rua Roma-tilde o Ramalho 59, 7000-671 Evora (Portugal)]. E-mail: smv@uevora.pt; Severino, Ricardo [Departamento de Matematica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)]. E-mail: ricardo@math.uminho.pt; Ramos, J. Sousa [Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049-001 Lisbon (Portugal)]. E-mail: sramos@math.ist.utl.pt

    2005-07-01

    We consider a class of boundary value problems for partial differential equations, whose solutions are, basically, characterized by the iteration of a nonlinear function. We apply methods of symbolic dynamics of discrete bimodal maps in the interval in order to give a topological characterization of its solutions.

  10. Group invariance in engineering boundary value problems

    CERN Document Server

    Seshadri, R

    1985-01-01

    REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Inte...

  11. Homology in Electromagnetic Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Matti Pellikka

    2010-01-01

    Full Text Available We discuss how homology computation can be exploited in computational electromagnetism. We represent various cellular mesh reduction techniques, which enable the computation of generators of homology spaces in an acceptable time. Furthermore, we show how the generators can be used for setting up and analysis of an electromagnetic boundary value problem. The aim is to provide a rationale for homology computation in electromagnetic modeling software.

  12. Boundary Value Problem for Black Rings

    CERN Document Server

    Morisawa, Yoshiyuki; Yasui, Yukinori

    2007-01-01

    We study the boundary value problem for asymptotically flat stationary black ring solutions to the five-dimensional vacuum Einstein equations. Assuming the existence of two additional commuting axial Killing vector fields and the horizon topology of $S^1\\times S^2$, we show that the only asymptotically flat black ring solution with a regular horizon is the Pomeransky-Sen'kov black ring solution.

  13. Geodesic boundary value problems with symmetry

    OpenAIRE

    Cotter, Colin; Holm, Darryl

    2010-01-01

    This paper shows how left and right actions of Lie groups on a manifold may be used to complement one another in a variational reformulation of optimal control problems equivalently as geodesic boundary value problems with symmetry. We prove an equivalence theorem to this effect and illustrate it with several examples. In finite-dimensions, we discuss geodesic flows on the Lie groups SO(3) and SE(3) under the left and right actions of their respective Lie algebras. In an infinite-dimensional ...

  14. The GPS-gravimetry boundary value problem

    Institute of Scientific and Technical Information of China (English)

    YU; Jinhai; ZHANG; Chuanding

    2005-01-01

    How to determine the earth's external gravity field with the accuracy of O(T2) by making use of GPS data and gravity values measured on the earth's surface is dealt with in this paper. There are two main steps: to extend these measured values on the earth's surface onto the reference ellipsoid at first and then to seek for the integral solution of the external Neumann problem outside the ellipsoid. In addition, the corresponding judging criteria of accuracy to solve the GPS-gravity boundary value problem are established. The integral solution given in the paper not only contains all frequency-spectral information of the gravity field with the accuracy of O(T2),but is also easily computed. In fact, the solution has great significance for both theory and practice.

  15. Complementary Lidstone Interpolation and Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2009-01-01

    Full Text Available We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P2m(t of degree 2m, which involves interpolating data at the odd-order derivatives. For P2m(t we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1th order differential equation and the complementary Lidstone boundary conditions.

  16. Spectral integration of linear boundary value problems

    CERN Document Server

    Viswanath, Divakar

    2012-01-01

    Spectral integration is a method for solving linear boundary value problems which uses the Chebyshev series representation of functions to avoid the numerical discretization of derivatives. It is occasionally attributed to Zebib (J. of Computational Physics vol. 53 (1984), p. 443-455) and more often to Greengard (SIAM J. on Numerical Analysis vol. 28 (1991), p. 1071-1080). Its advantage is believed to be its relative immunity to errors that arise when nearby grid points are used to approximate derivatives. In this paper, we reformulate the method of spectral integration by changing it in four different ways. The changes consist of a more convenient integral formulation, a different way to treat and interpret boundary conditions, treatment of higher order problems in factored form, and the use of piecewise Chebyshev grid points. Our formulation of spectral integration is more flexible and powerful as show by its ability to solve a problem that would otherwise take 8192 grid points using only 96 grid points. So...

  17. Boundary value problems and Markov processes

    CERN Document Server

    Taira, Kazuaki

    2009-01-01

    This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov pr...

  18. A selfadjoint hyperbolic boundary-value problem

    Directory of Open Access Journals (Sweden)

    Nezam Iraniparast

    2003-02-01

    Full Text Available We consider the eigenvalue wave equation $$u_{tt} - u_{ss} = lambda pu,$$ subject to $ u(s,0 = 0$, where $uinmathbb{R}$, is a function of $(s, t in mathbb{R}^2$, with $tge 0$. In the characteristic triangle $T ={(s,t:0leq tleq 1, tleq sleq 2-t}$ we impose a boundary condition along characteristics so that $$ alpha u(t,t-beta frac{partial u}{partial n_1}(t,t = alpha u(1+t,1-t +betafrac{partial u}{partial n_2}(1+t,1-t,quad 0leq tleq1. $$ The parameters $alpha$ and $beta$ are arbitrary except for the condition that they are not both zero. The two vectors $n_1$ and $n_2$ are the exterior unit normals to the characteristic boundaries and $frac{partial u}{partial n_1}$, $frac{partial u}{partial n_2}$ are the normal derivatives in those directions. When $pequiv 1$ we will show that the above characteristic boundary value problem has real, discrete eigenvalues and corresponding eigenfunctions that are complete and orthogonal in $L_2(T$. We will also investigate the case where $pgeq 0$ is an arbitrary continuous function in $T$.

  19. Symmetry approach in boundary value problems

    OpenAIRE

    Habibullin, I. T.

    1995-01-01

    The problem of construction of the boundary conditions for nonlinear equations is considered compatible with their higher symmetries. Boundary conditions for the sine-Gordon, Jiber-Shabat and KdV equations are discussed. New examples are found for the Jiber-Shabat equation.

  20. Boundary value problems on product domains

    OpenAIRE

    Ehsani, Dariush

    2005-01-01

    We consider the inhomogeneous Dirichlet problem on product domains. The main result is the asymptotic expansion of the solution in terms of increasing smoothness up to the boundary. In particular, we show the exact nature of the singularities of the solution at singularities of the boundary by constructing singular functions which make up an asymptotic expansion of the solution.

  1. Geodesic boundary value problems with symmetry

    CERN Document Server

    Cotter, C J

    2009-01-01

    This paper shows how left and right actions of Lie groups on a manifold may be used to complement one another in a variational reformulation of optimal control problems equivalently as geodesic boundary value problems with symmetry. We prove an equivalence theorem to this effect and illustrate it with several examples. In finite-dimensions, we discuss geodesic flows on the Lie groups SO(3) and SE(3) under the left and right actions of their respective Lie algebras. In an infinite-dimensional example, we discuss optimal large-deformation matching of one closed curve to another embedded in the same plane. In the curve-matching example, the manifold $\\Emb(S^1, \\mathbb{R}^2)$ comprises the space of closed curves $S^1$ embedded in the plane $\\mathbb{R}^2$. The diffeomorphic left action $\\Diff(\\mathbb{R}^2)$ deforms the curve by a smooth invertible time-dependent transformation of the coordinate system in which it is embedded, while leaving the parameterisation of the curve invariant. The diffeomorphic right action...

  2. Spherical gravitational curvature boundary-value problem

    Science.gov (United States)

    Šprlák, Michal; Novák, Pavel

    2016-08-01

    Values of scalar, vector and second-order tensor parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third-order tensor spherical harmonics. Secondly, gravitational curvature boundary-value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub-integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so-called Meissl scheme, i.e., an important theoretical framework that relates various parameters of the Earth's gravitational field.

  3. Boundary Value Problems Arising in Kalman Filtering

    OpenAIRE

    Sinem Ertürk; Zeka Mazhar; Agamirza Bashirov

    2008-01-01

    The classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic) with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value probl...

  4. State-dependent impulses boundary value problems on compact interval

    CERN Document Server

    Rachůnková, Irena

    2015-01-01

    This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary...

  5. Partial differential equations IX elliptic boundary value problems

    CERN Document Server

    Egorov, Yu; Shubin, M

    1997-01-01

    This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.

  6. Free Boundary Value Problems for Abstract Elliptic Equations and Applications

    Institute of Scientific and Technical Information of China (English)

    Veli SHAKHMUROV

    2011-01-01

    The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract Lp-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.

  7. Solvability of a nonlinear boundary value problem

    Directory of Open Access Journals (Sweden)

    S. Peres

    2013-01-01

    Full Text Available We study the existence and multiplicity of positive solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions where both of the nonlinearities are of power type.

  8. Boundary value problems and Fourier expansions

    CERN Document Server

    MacCluer, Charles R

    2004-01-01

    Based on modern Sobolev methods, this text for advanced undergraduates and graduate students is highly physical in its orientation. It integrates numerical methods and symbolic manipulation into an elegant viewpoint that is consonant with implementation by digital computer. The first five sections form an informal introduction that develops students' physical and mathematical intuition. The following section introduces Hilbert space in its natural environment, and the next six sections pose and solve the standard problems. The final seven sections feature concise introductions to selected topi

  9. Positive Solutions for Boundary Value Problems with Fractional Order

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2013-02-01

    Full Text Available In this paper we investigate the existence of at least one, two positive solutions by using the Krasnoselskii fixed-point theorem in cones for nonlinear boundary value problem with fractional order.

  10. Positive Solutions for Higher Order Singular -Laplacian Boundary Value Problems

    Indian Academy of Sciences (India)

    Guoliang Shi; Junhong Zhang

    2008-05-01

    This paper investigates $2m-\\mathrm{th}(m≥ 2)$ order singular -Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2-th order singular -Laplacian BVPs on closed interval.

  11. BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.

  12. Boundary value problems of discrete generalized Emden-Fowler equation

    Institute of Scientific and Technical Information of China (English)

    YU; Jianshe; GUO; Zhiming

    2006-01-01

    By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.

  13. Solvability of a fourth order boundary value problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Chaitan P. Gupta

    1988-01-01

    Full Text Available Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary conditions.

  14. Solvability of a fourth order boundary value problem with periodic boundary conditions

    OpenAIRE

    Chaitan P. Gupta

    1988-01-01

    Fourth order boundary value problems arise in the study of the equilibrium of an elastaic beam under an external load. The author earlier investigated the existence and uniqueness of the solutions of the nonlinear analogues of fourth order boundary value problems that arise in the equilibrium of an elastic beam depending on how the ends of the beam are supported. This paper concerns the existence and uniqueness of solutions of the fourth order boundary value problems with periodic boundary co...

  15. Modified Differential Transform Method for Two Singular Boundary Values Problems

    Directory of Open Access Journals (Sweden)

    Yinwei Lin

    2014-01-01

    Full Text Available This paper deals with the two singular boundary values problems of second order. Two singular points are both boundary values points of the differential equation. The numerical solutions are developed by modified differential transform method (DTM for expanded point. Linear and nonlinear models are solved by this method to get more reliable and efficient numerical results. It can also solve ordinary differential equations where the traditional one fails. Besides, we give the convergence of this new method.

  16. Integral Formulation of the Boundary Value Problem in Waveguides.

    Science.gov (United States)

    Sancho, M.

    1980-01-01

    Presents an integral approach to the boundary value problem in waveguides deduced from the Kirchoff's integral formulation of the electromagnetic field. Also, the basis for the numerical solution of more general problems is given, including the example of the isosceles right triangular guide. (Author/SK)

  17. Local solution for a class of mixed boundary value problems

    International Nuclear Information System (INIS)

    A local method is developed for solving locally partial differential equations with mixed boundary conditions. The method is based on a heuristic idea, properties of diffusion processes, stopping times and the Ito formula for semimartingales. According to the heuristic idea, the diffusion process used for solving locally a partial differential with mixed boundary conditions is stopped when it reaches a Neumann boundary and then restarted inside the domain of definition of this equation at a point depending on the Neumann conditions. The proposed method is illustrated and its accuracy assessed by two simple numerical examples solving locally mixed boundary value problems in one and two space dimensions

  18. Nonlinear Second-Order Multivalued Boundary Value Problems

    Indian Academy of Sciences (India)

    Leszek Gasiński; Nikolaos S Papageorgiou

    2003-08-01

    In this paper we study nonlinear second-order differential inclusions involving the ordinary vector -Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operatory theory and from multivalued analysis, we obtain solutions for both the `convex' and `nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.

  19. On weak solvability of boundary value problems for elliptic systems

    OpenAIRE

    Ponce, Felipe; Lebedev, Leonid,; Rendón, Leonardo,

    2013-01-01

    This paper concerns with existence and uniqueness of a weak solution for elliptic systems of partial differential equations with mixed boundary conditions. The proof is based on establishing the coerciveness of bilinear forms, related with the system of equations, which depend on first-order derivatives of vector functions in Rn. The condition of coerciveness relates to Korn's type inequalities. The result is illustrated by an example of boundary value problems for a class of elliptic equatio...

  20. Solvability for fractional order boundary value problems at resonance

    OpenAIRE

    Hu Zhigang; Liu Wenbin

    2011-01-01

    Abstract In this paper, by using the coincidence degree theory, we consider the following boundary value problem for fractional differential equation D 0 + α x ( t ) = f ( t , x ( t ) , x ′ ( t ) , x ″ ( t ) ) , t ∈ [ 0 , 1 ] , x ( 0 ) = x ( 1 ) , x ′ ( 0 ) = x ″ ( 0 ) = 0 , where D 0 + α denotes the Caputo fractional differential o...

  1. Robust Monotone Iterates for Nonlinear Singularly Perturbed Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boglaev Igor

    2009-01-01

    Full Text Available This paper is concerned with solving nonlinear singularly perturbed boundary value problems. Robust monotone iterates for solving nonlinear difference scheme are constructed. Uniform convergence of the monotone methods is investigated, and convergence rates are estimated. Numerical experiments complement the theoretical results.

  2. Fourth-order discrete anisotropic boundary-value problems

    Directory of Open Access Journals (Sweden)

    Maciej Leszczynski

    2015-09-01

    Full Text Available In this article we consider the fourth-order discrete anisotropic boundary value problem with both advance and retardation. We apply the direct method of the calculus of variations and the mountain pass technique to prove the existence of at least one and at least two solutions. Non-existence of non-trivial solutions is also undertaken.

  3. Riemann boundary value problem for triharmonic equation in higher space.

    Science.gov (United States)

    Gu, Longfei

    2014-01-01

    We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ(3)[u](x) = 0, x ∈ R (n)\\∂Ω, u (+)(x) = u (-)(x)G(x) + g(x), x ∈ ∂Ω, (D (j) u)(+)(x) = (D (j) u)(-)(x)A j + f j (x), x ∈ ∂Ω, u(∞) = 0, where (j = 1,…, 5)  ∂Ω is a Lyapunov surface in R (n) , D = ∑ k=1 (n) e k (∂/∂x k) is the Dirac operator, and u(x) = ∑ A e A u A (x) are unknown functions with values in a universal Clifford algebra Cl(V n,n). Under some hypotheses, it is proved that the boundary value problem has a unique solution. PMID:25114963

  4. Solution of Boundary-Value Problems using Kantorovich Method

    Science.gov (United States)

    Gusev, A. A.; Hai, L. L.; Chuluunbaatar, O.; Vinitsky, S. I.; Derbov, V. L.

    2016-02-01

    We propose a computational scheme for solving the eigenvalue problem for an elliptic differential equation in a two-dimensional domain with Dirichlet boundary conditions. The solution is sought in the form of Kantorovich expansion over the basis functions of one of the independent variables with the second variable treated as a parameter. The basis functions are calculated as solutions of the parametric eigenvalue problem for an ordinary second-order differential equation. As a result, the initial problem is reduced to a boundary-value problem for a set of self-adjoint second-order differential equations for functions of the second independent variable. The discrete formulation of the problem is implemented using the finite element method with Hermite interpolation polynomials. The effciency of the calculation scheme is shown by benchmark calculations for a square membrane with a degenerate spectrum.

  5. Solution of Boundary-Value Problems using Kantorovich Method

    Directory of Open Access Journals (Sweden)

    Gusev A.A.

    2016-01-01

    Full Text Available We propose a computational scheme for solving the eigenvalue problem for an elliptic differential equation in a two-dimensional domain with Dirichlet boundary conditions. The solution is sought in the form of Kantorovich expansion over the basis functions of one of the independent variables with the second variable treated as a parameter. The basis functions are calculated as solutions of the parametric eigenvalue problem for an ordinary second-order differential equation. As a result, the initial problem is reduced to a boundary-value problem for a set of self-adjoint second-order differential equations for functions of the second independent variable. The discrete formulation of the problem is implemented using the finite element method with Hermite interpolation polynomials. The effciency of the calculation scheme is shown by benchmark calculations for a square membrane with a degenerate spectrum.

  6. SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR SEMI-LINEAR RETARDED DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    任景莉; 葛渭高

    2003-01-01

    A boundary value problems f or functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given.

  7. Linear boundary value problems for differential algebraic equations

    OpenAIRE

    Balla, Katalin; März, Roswitha

    2003-01-01

    By the use of the corresponding shift matrix, the paper gives a criterion for the unique solvability of linear boundary value problems posed for linear differential algebraic equations up to index 2 with well-matched leading coefficients. The solution is constructed by a proper Green function. Another characterization of the solutions is based upon the description of arbitrary affine linear subspaces of solutions to linear differential algebraic equations in terms of solutions to the adjoint ...

  8. Boundary value problems with incremental plasticity in granular media

    Science.gov (United States)

    Chung, T. J.; Lee, J. K.; Costes, N. C.

    1974-01-01

    Discussion of the critical state concept in terms of an incremental theory of plasticity in granular (soil) media, and formulation of the governing equations which are convenient for a computational scheme using the finite element method. It is shown that the critical state concept with its representation by the classical incremental theory of plasticity can provide a powerful means for solving a wide variety of boundary value problems in soil media.

  9. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

    International Nuclear Information System (INIS)

    The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H (Ω) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs

  10. A CLASS OF NONLINEAR SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    Mo Jiaqi

    2007-01-01

    A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.

  11. Periodic and boundary value problems for second order differential inclusions

    Directory of Open Access Journals (Sweden)

    Michela Palmucci

    2001-01-01

    Full Text Available In this paper we study differential inclusions with boundary conditions in which the vector field F(t,x,y is a multifunction with Caratheodory type conditions. We consider, first, the case which F has values in ℝ and we establish the existence of extremal solutions in the order interval determined by the lower and the upper solution. Then we prove the existence of solutions for a Dirichlet problem in the case in which F takes their values in a Hilbert space.

  12. Fractional Extensions of some Boundary Value Problems in Oil Strata

    Indian Academy of Sciences (India)

    Mridula Garg; Alka Rao

    2007-05-01

    In the present paper, we solve three boundary value problems related to the temperature field in oil strata - the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.

  13. Boundary-value problems for x-analytical functions with weighted boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Kapshivyi, A.A. [Kiev Univ. (Ukraine)

    1994-11-10

    We consider boundary-value problems for x-analytical functions of a complex variable z = x + iy in a number of domains. Limit values with the weight (ln x){sup {minus}1} are given for the real part of the x-analytical function on the sections of the boundary that follow the imaginary axis, and simple limits are given for the real part of the x-analytical functions on the part of the boundary outside the imaginary axis. The apparatus of integral representations of x-analytical functions is applied to obtain a solution of the problem in quadratures.

  14. STABILITY OF A KIND OF COMPOUND BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the perturbation of boundary curve.

  15. An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Mohammad Maleki

    2012-01-01

    Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.

  16. Monotone positive solution for three-point boundary value problem

    Institute of Scientific and Technical Information of China (English)

    SUN Yong-ping

    2008-01-01

    In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied:x"(t)+f(t,x(t))=0,0

  17. Partial differential equations & boundary value problems with Maple

    CERN Document Server

    Articolo, George A

    2009-01-01

    Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327  Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...

  18. The boundary value problem for discrete analytic functions

    KAUST Repository

    Skopenkov, Mikhail

    2013-06-01

    This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

  19. The Nonlinear Predator-Prey Singularly Perturbed Robin Initial Boundary Value Problems for Reaction Diffusion System

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2003-01-01

    The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.

  20. A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations

    CERN Document Server

    Alikhanov, A A

    2011-01-01

    We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.

  1. SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

    Institute of Scientific and Technical Information of China (English)

    MoJiaqi

    2002-01-01

    The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem,the asymptotic behavior of solution for the boundary value problem is studied.

  2. Dirichlet-Neumann bracketing for boundary-value problems on graphs

    Directory of Open Access Journals (Sweden)

    Sonja Currie

    2005-08-01

    Full Text Available We consider the spectral structure of second order boundary-value problems on graphs. A variational formulation for boundary-value problems on graphs is given. As a consequence we can formulate an analogue of Dirichlet-Neumann bracketing for boundary-value problems on graphs. This in turn gives rise to eigenvalue and eigenfunction asymptotic approximations.

  3. First and second fundamental boundary value problems of spiral plate

    International Nuclear Information System (INIS)

    Complex variable methods and Laplace and Riemann-Milne transforms are used to solve the first and second fundamental boundary problems of the spiral plate. The Goursat functions are derived in closed form. The case of the wedge plate is included as a special case. (author)

  4. Solvability of a fourth-order boundary value problem with periodic boundary conditions II

    OpenAIRE

    Chaitan P. Gupta

    1991-01-01

    Let f:[0,1]×R4→R be a function satisfying Caratheodory's conditions and e(x)∈L1[0,1]. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d4udx4+f(x,u(x),u′(x),u″(x),u‴(x))=e(x),   0

  5. PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

    Institute of Scientific and Technical Information of China (English)

    Chen Guowang; Xue Hongxia

    2008-01-01

    In this article, the existence, uniqueness and regularities of the global gener-alized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt -uxx-auxxtt+bux4 - duxxt= f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

  6. Ray tracing in relativistic astrometry: the boundary value problem

    International Nuclear Information System (INIS)

    Relativistic astrometry has recently become an active field of research owing to new observational technologies which allow for accuracies of a microarcsecond. To assure this accuracy in data analysis, one has to perform ray tracing in a general relativistic framework including terms of the order of (v/c)3 in the weak field treatment of Einstein equations applied to the solar system. Basic to the solution of a ray tracing problem are the boundary conditions that one has to fix from the observational data. In this paper we solve this problem to (v/c)3 in a fully analytical way

  7. A kernel-free boundary integral method for elliptic boundary value problems

    Science.gov (United States)

    Ying, Wenjun; Henriquez, Craig S.

    2007-12-01

    This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.

  8. Existence of Positive Solutions for Higher Order Boundary Value Problem on Time Scales

    Institute of Scientific and Technical Information of China (English)

    XIE DA-PENG; LIU YANG; SUN MING-ZHE; Li Yong

    2013-01-01

    In this paper,we investigate the existence of positive solutions of a class higher order boundary value problems on time scales.The class of boundary value problems educes a four-point (or three-point or two-point) boundary value problems,for which some similar results are established.Our approach relies on the Krasnosel'skii fixed point theorem.The result of this paper is new and extends previously known results.

  9. An initial-boundary value problem for three-dimensional Zakharov-Kuznetsov equation

    Science.gov (United States)

    Faminskii, Andrei V.

    2016-02-01

    An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain weighted spaces are established.

  10. 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.

  11. ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

    Institute of Scientific and Technical Information of China (English)

    A.S. BERDYSHEV; A. CABADA; B.Kh. TURMETOV

    2014-01-01

    This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.

  12. Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Topal SGulsan

    2009-01-01

    Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.

  13. Existence of Solutions of Periodic Boundary Value Problems for Impulsive Functional Duffing Equations at Nonresonance Case

    Directory of Open Access Journals (Sweden)

    Liu Yuji

    2008-01-01

    Full Text Available Abstract This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: . Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results.

  14. m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.

  15. Boundary value problem for the linearized Boltzmann equation in a weakly ionized plasma

    International Nuclear Information System (INIS)

    A simulated problem for transport of charged particles in a neutral gas and weakly ionized plasma is considered. Boundary value problem for the model is formulated and its estimation by a given boundary function is performed. Galerkin method is applied for obtaining an approximate solution of the problem. (author)

  16. Boundary value problems on the half line in the theory of colloids

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2002-01-01

    Full Text Available We present existence results for some boundary value problems defined on infinite intervals. In particular our discussion includes a problem which arises in the theory of colloids.

  17. On solvability of some boundary value problems for a biharmonic equation with periodic conditions

    Science.gov (United States)

    Karachik, Valery V.; Massanov, Saparbay K.; Turmetov, Batirkhan Kh.

    2016-08-01

    In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.

  18. A boundary value problem for first order strictly hyperbolic systems on the plane

    Science.gov (United States)

    Soldatov, Alexander P.; Zhura, Nikolay A.

    2015-11-01

    Boundary value problems, more precisely Dirichlet's problem for a string equation, or for an equivalent system of first order equations have been first studied in the first half of last century ([1] - [9]). The interest to these problems has been big ever since, see e.g. [10, 11]. All these papers have looked into the boundary value problems in a finite domains in the plane. Strictly hyperbolic systems with more than two characteristics in infinite domains, have been studied in [12, 13]. The question of boundary value problems for a hyperbolic system of equations with more than two characteristics in finite domain on the plane, when a boundary conditions are prescribed at a whole boundary of the domain, evidently remained open. In this paper, we study this problem in a finite domain on the plane for a hyperbolic system of equations of the first order with constant coefficients and with three mutually distinct characteristics.

  19. Variation-difference method for solving boundary value problems for linear elliptic complex equations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound boundary value problem for the complex equations of the first order is discussed. The approximate solutions of the boundary value problem are found by the variation-difference method, and the error estimates for the approximate solutions are derived.Finally the approximate method of the oblique derivative problem for linear uniformly elliptic equations of the second or der is introduced.

  20. Electromagnetic wave theory for boundary-value problems an advanced course on analytical methods

    CERN Document Server

    Eom, Hyo J

    2004-01-01

    Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As such, Electromagnetic Wave Theory for Boundary-Value Problems is intended to help students enhance analytic skills by solving pertinent boundary-value problems. In particular, the techniques of Fourier transform, mode matching, and residue calculus are utilized to solve some canonical scattering and radiation problems.

  1. Local existence of solution to free boundary value problem for compressible Navier-Stokes equations

    OpenAIRE

    Liu, Jian

    2015-01-01

    This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. A local (in time) existence of weak solution is established, in particular, the density is positive and the solution is regular away from the free boundary.

  2. Mixed Boundary Value Problems for Stationary Magnetohydrodynamic Equations of a Viscous Heat-Conducting Fluid

    Science.gov (United States)

    Alekseev, Gennady

    2016-04-01

    We consider the boundary value problem for stationary magnetohydrodynamic equations of electrically and heat conducting fluid under inhomogeneous mixed boundary conditions for electromagnetic field and temperature and Dirichlet condition for the velocity. The problem describes the thermoelectromagnetic flow of a viscous fluid in 3D bounded domain with the boundary consisting of several parts with different thermo- and electrophysical properties. The global solvability of the boundary value problem is proved and the apriori estimates of the solution are derived. The sufficient conditions on the data are established which provide a local uniqueness of the solution.

  3. Periodic and Boundary Value Problems for Second Order Differential Equations

    Indian Academy of Sciences (India)

    Nikolaos S Papageorgiou; Francesca Papalini

    2001-02-01

    In this paper we study second order scalar differential equations with Sturm–Liouville and periodic boundary conditions. The vector field (, , ) is Caratheodory and in some instances the continuity condition on or is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.

  4. The boundary value problems for the scalar Oseen equation

    Czech Academy of Sciences Publication Activity Database

    Medková, Dagmar; Skopin, E.; Varnhorn, W.

    2012-01-01

    Roč. 285, 17-18 (2012), s. 2208-2221. ISSN 0025-584X R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : scalar Oseen equation * Dirichlet problem * Neumann problem Subject RIV: BA - General Mathematics Impact factor: 0.576, year: 2012 http://onlinelibrary.wiley.com/doi/10.1002/mana.201100219/abstract

  5. Boundary value problems for the Helmholtz equation in a half-plane

    OpenAIRE

    Chandler-Wilde, SN

    1994-01-01

    The Dirichlet and impedance boundary value problems for the Helmholtz equation in a half-plane with bounded continuous boundary data are studied. For the Dirichlet problem the solution can be constructed explicitly. We point out that, for wavenumbers k > 0, the solution, although it satisfies a limiting absorption principle, may increase in magnitude with distance from the boundary. Using the explicit solution we propose a novel radiation condition which we utilise in formulating the impedanc...

  6. Resonance and multiplicity in periodic boundary value problems with singularity

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan; Vrkoč, Ivo

    2003-01-01

    Roč. 128, č. 1 (2003), s. 45-70. ISSN 0862-7959 R&D Projects: GA ČR GA201/01/1451; GA ČR GA201/01/1199 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : second order nonlinear ordinary differential equation * periodic problem * lower and upper functions Subject RIV: BA - General Mathematics

  7. On Neumann boundary value problems for some quasilinear elliptic equations

    Directory of Open Access Journals (Sweden)

    Paul A. Binding

    1997-01-01

    Full Text Available function $a(x$ on the existence of positive solutions to the problem $$left{ eqalign{ -{ m div},(|abla u|^{p-2}abla u&= lambda a(x|u|^{p-2}u+b(x|u|^{gamma-2}u, quad xinOmega, cr x{partial u overpartial n}&=0, quad xinpartialOmega,,} ight. $$ where $Omega$ is a smooth bounded domain in $R^n$, $b$ changes sign, $1problem has a positive solution. (ii if $int_Omega a(x, dx=0$, then the problem has a positive solution for small $lambda$ provided that $int_Omega b(x,dx<0$.

  8. Asymptotic Solution of the Theory of Shells Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    I. V. Andrianov

    2007-01-01

    Full Text Available This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i it is devoted to the fundamental principles of asymptotic approaches, and (ii it deals with both traditional approaches, and less widely used, new approaches. The authors have paid special attention to examples and discussion of results rather than to burying the ideas in formalism, notation, and technical details.

  9. Existence of three positive solutions for boundary value problem with fractional order and infinite delay

    Directory of Open Access Journals (Sweden)

    Benaouda Hedia

    2015-07-01

    Full Text Available In this paper we investigate the existence three positives solutions by using Leggett-Williams fixed point theorem in cones for three boundary value problem with fractional order and infinite delay.

  10. Existence Results for Higher-Order Boundary Value Problems on Time Scales

    OpenAIRE

    Sang Yanbin; Liu Jian

    2009-01-01

    By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales , ; , ; , ; , , where , , , , , , , and is rd-continuous.

  11. A Global Description of the Positive Solutions of Sublinear Second-Order Discrete Boundary Value Problems

    OpenAIRE

    Ma Ruyun; Xu Youji; Gao Chenghua

    2009-01-01

    Let be an integer with , , . We consider boundary value problems of nonlinear second-order difference equations of the form , , , where , and, for , and , , . We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.

  12. On a periodic boundary value problem for second-order linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    2005-01-01

    Roč. 3, - (2005), s. 247-261. ISSN 1687-2762 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics

  13. On the Approximate Controllability of Some Semilinear Parabolic Boundary-Value Problems

    International Nuclear Information System (INIS)

    We prove the approximate controllability of several nonlinear parabolic boundary-value problems by means of two different methods: the first one can be called a Cancellation method and the second one uses the Kakutani fixed-point theorem

  14. Positive solutions for a third-order three-point boundary-value problem

    OpenAIRE

    Torres, Francisco J.

    2013-01-01

    In this article, we study the existence of positive solutions to a nonlinear third-order three point boundary value problem. The main tools are Krasnosel'skii fixed point theorem on cones, and the fixed point index theory.

  15. Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Zhao Ya-Hong

    2010-01-01

    Full Text Available We investigate the following nonlinear first-order periodic boundary value problem on time scales: , , . Some new existence criteria of positive solutions are established by using the monotone iterative technique.

  16. 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.

  17. Existence and uniqueness of solutions for a Neumann boundary-value problem

    Directory of Open Access Journals (Sweden)

    Safia Benmansour

    2011-09-01

    Full Text Available In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general $alpha$-concave operators.

  18. Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Moulay Rchid Sidi Ammi

    2013-01-01

    Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.

  19. Closed form solution to a second order boundary value problem and its application in fluid mechanics

    International Nuclear Information System (INIS)

    The Adomian decomposition method is used by many researchers to investigate several scientific models. In this Letter, the modified Adomian decomposition method is applied to construct a closed form solution for a second order boundary value problem with singularity

  20. Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity

    Science.gov (United States)

    Patnaik, Surya N.; Kaljevic, Igor; Hopkins, Dale A.; Saigal, Sunil

    1995-01-01

    In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.

  1. Well-posed initial-boundary value problems for the Zakharov-Kuznetsov equation

    Directory of Open Access Journals (Sweden)

    Andrei V. Faminskii

    2008-09-01

    Full Text Available This paper deals with non-homogeneous initial-boundary value problems for the Zakharov-Kuznetsov equation, which is one of the variants of multidimensional generalizations of the Korteweg-de Vries equation. Results on local and global well-posedness are established in a scale of Sobolev-type spaces under natural assumptions on initial and boundary data.

  2. Boundary value problems and the validity of the Post constraint in modern electromagnetism

    OpenAIRE

    Lakhtakia, Akhlesh

    2005-01-01

    When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the chosen material and a naive application of the usual boundary conditions. It is shown here that the conflict vanishes when the boundary conditions are properly derived from the fundamental equations, and the validity of the Post constraint in modern macroscop...

  3. Dirichlet boundary-value problem for Chern-Simons modified gravity

    International Nuclear Information System (INIS)

    Chern-Simons modified gravity comprises the Einstein-Hilbert action and a higher-derivative interaction containing the Chern-Pontryagin density. We derive the analog of the Gibbons-Hawking-York boundary term required to render the Dirichlet boundary-value problem well defined. It turns out to be a boundary Chern-Simons action for the extrinsic curvature. We address applications to black hole thermodynamics.

  4. Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval

    Directory of Open Access Journals (Sweden)

    Andrei V. Faminskii

    2010-01-01

    Full Text Available This paper studies nonhomogeneous initial-boundary value problems for quasilinear one-dimensional odd-order equations posed on a bounded interval. For reasonable initial and boundary conditions we prove existence and uniqueness of global weak and regular solutions. Also we show the exponential decay of the obtained solution with zero boundary conditions and right-hand side, and small initial data.

  5. Application of the homotopy perturbation method to linear and nonlinear fourth-order boundary value problems

    International Nuclear Information System (INIS)

    In this study, we applied the homotopy perturbation (HP) method for solving linear and nonlinear fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of a convergent series with easily computable components. Comparisons between the results of the HP method and the analytical solution showed that this method gives very precise results with a few terms. In the implied HP method, some unknown parameters in the initial guess are introduced, which are identified after applying boundary conditions. This improvement results in higher accuracy

  6. Application of the homotopy perturbation method to linear and nonlinear fourth-order boundary value problems

    Energy Technology Data Exchange (ETDEWEB)

    Roohi, Ehsan; Marzabadi, Faezeh Rasi [Aerospace Research Institute, PO Box 14665-834, Tehran (Iran, Islamic Republic of); Farjami, Yagoub [Department of Aerospace Engineering, Sharif University of Technology, PO Box 11365-8639, Azadi Ave., Tehran (Iran, Islamic Republic of)], E-mail: Ehsan.roohi@gmail.com

    2008-05-15

    In this study, we applied the homotopy perturbation (HP) method for solving linear and nonlinear fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of a convergent series with easily computable components. Comparisons between the results of the HP method and the analytical solution showed that this method gives very precise results with a few terms. In the implied HP method, some unknown parameters in the initial guess are introduced, which are identified after applying boundary conditions. This improvement results in higher accurac000.

  7. Verification example of modeling corps equipment construction for boundary value problem for tense deformation solution

    International Nuclear Information System (INIS)

    Comparative analysis of results of the theoretical decision for the boundary-value problem obtained in the context of the theory of plates and shells, and decision by the boundary element method using CAN program is presented. Stressed deformed state of the internal pressure loaded thin-walled cylindrical shell with thin round plates (bottom) on ends was considered as an example. The considered boundary-value problem may be used as test example for the verification of programs used for the validation of nuclear park safety

  8. Mixed boundary value problems for the stationary magnetohydrodynamics model of a viscous heat-conducting fluid

    Science.gov (United States)

    Alekseev, G. V.

    2015-12-01

    The boundary value problem for the stationary magnetohydrodynamics model of a viscous heatconducting fluid considered under inhomogeneous mixed boundary conditions for an electromagnetic field and the temperature and Dirichlet condition for the velocity is investigated. This problem describes the flow of an electricaland heat-conducting liquid in a bounded three-dimensional domain the boundary of which consists of several parts with different thermoand electrophysical properties. Sufficient conditions imposed on the initial data to provide for global solvability of the problem and local uniqueness of its solution are established.

  9. SUPORT, Solution of Linear 2 Point Boundary Value Problems, Runge-Kutta-Fehlberg Method

    International Nuclear Information System (INIS)

    1 - Description of problem or function: SUPORT solves a system of linear two-point boundary-value problems subject to general separated boundary conditions. 2 - Method of solution: The method of solution uses superposition coupled with an ortho-normalization procedure and a variable-step Runge-Kutta-Fehlberg integration scheme. Each time the superposition solutions start to lose their numerical independence, the vectors are re-ortho-normalized before integration proceeds. The underlying principle of the algorithm is then to piece together the intermediate (orthogonalized) solutions, defined on the various subintervals, to obtain the desired solution. 3 - Restrictions on the complexity of the problem: The boundary-value problem must be linear and the boundary conditions must be separated. The number of equations which can be solved is dependent upon the main storage available

  10. Nonlinear boundary value problems for first order impulsive integro-differential equations

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1989-01-01

    Full Text Available In this paper, we investigate a class of first order impulsive integro-differential equations subject to certain nonlinear boundary conditions and prove, with the help of upper and lower solutions, that the problem has a solution lying between the upper and lower solutions. We also develop monotone iterative technique and show the existence of multiple solutions of a class of periodic boundary value problems.

  11. On Initial-Boundary Value Problem of Stochastic Heat Equation in a Lipschitz Cylinder

    CERN Document Server

    Chang, Tongkeun; Yang, Minsuk

    2011-01-01

    We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero cylinder condition. We prove a regularity result after finding suitable spaces for the solution and the pre-assigned datum in the problem. The tools from potential theory, harmonic analysis and probability are used. Some Lemmas are as important as the main Theorem.

  12. An Efficient Method Based on Lucas Polynomials for Solving High-Order Linear Boundary Value Problems

    OpenAIRE

    Çetin, Muhammed; Sezer, Mehmet; Kocayiğit, Hüseyin

    2015-01-01

    In this paper, a new collocation method based on Lucas polynomials for solving high-order linear differential equations with variable coefficients under the boundary conditions is presented by transforming the problem into a system of linear algebraic equations with Lucas coefficients. The proposed approach is applied to fourth, fifth, sixth and eighth-order two-point boundary values problems occurring in science and engineering, and compared by existing methods. The technique gives better ap...

  13. Existence of Solutions for p-Laplace Equations Subjected to Neumann Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    HU Zhi-gang; RUI Wen-juan; LIU Wen-bing

    2006-01-01

    The existence of solutions for one dimensional p-Laplace equation (φp(u'))'=f(t,u,u') with t∈(0,1) and φp(s)=│s│p-2s,s≠0 subjected to Neumann boundary value problem at u'(0)=0,u'(1)=0. By using the degree theory, the sufficient conditions of the existence of solutions for p-Laplace equation subjected to Neumann boundary value condition are established.

  14. Nonlinear second order system of Neumann boundary value problems at resonance

    Directory of Open Access Journals (Sweden)

    Chaitan P. Gupta

    1989-01-01

    Full Text Available Let f:[0,π]×ℝN→ℝN, (N≥1 satisfy Caratheodory conditions, e(x∈L1([0,π];ℝN. This paper studies the system of nonlinear Neumann boundary value problems x″(t+f(t,x(t=e(t, 0problem is at resonance since the associated linear boundary value problem x″(t=λx(t, 0boundary value problems.

  15. Direct approach for solving nonlinear evolution and two-point boundary value problems

    Indian Academy of Sciences (India)

    Jonu Lee; Rathinasamy Sakthivel

    2013-12-01

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples including time-delayed nonlinear Burgers equation to illustrate the validity and the great potential of the differential transform method. Numerical experiments demonstrate the use and computational efficiency of the method. This method can easily be applied to many nonlinear problems and is capable of reducing the size of computational work.

  16. Two-scale homogenization of electromechanically coupled boundary value problems. Consistent linearization and applications

    Science.gov (United States)

    Schröder, Jörg; Keip, Marc-André

    2012-08-01

    The contribution addresses a direct micro-macro transition procedure for electromechanically coupled boundary value problems. The two-scale homogenization approach is implemented into a so-called FE2-method which allows for the computation of macroscopic boundary value problems in consideration of microscopic representative volume elements. The resulting formulation is applicable to the computation of linear as well as nonlinear problems. In the present paper, linear piezoelectric as well as nonlinear electrostrictive material behavior are investigated, where the constitutive equations on the microscale are derived from suitable thermodynamic potentials. The proposed direct homogenization procedure can also be applied for the computation of effective elastic, piezoelectric, dielectric, and electrostrictive material properties.

  17. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  18. Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems

    OpenAIRE

    Xu Jia; Han XiaoLing

    2010-01-01

    We consider the fourth-order two-point boundary value problem , , , where is a parameter, is given constant, with on any subinterval of , satisfies for all , and , , for some . By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem.

  19. Solvability of Boundary Value Problem at Resonance for Third-Order Functional Differential Equations

    Indian Academy of Sciences (India)

    Pinghua Yang; Zengji Du; Weigao Ge

    2008-05-01

    This paper is devoted to the study of boundary value problem of third-order functional differential equations. We obtain some existence results for the problem at resonance under the condition that the nonlinear terms is bounded or generally unbounded. In this paper we mainly use the topological degree theory.

  20. Numerical analysis of fourth-order boundary value problems in fluid mechanics and mathematics

    DEFF Research Database (Denmark)

    Hosseinzadeh, Elham; Barari, Amin; Fouladi, Fama;

    2010-01-01

    In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

  1. Numerical Analysis of Forth-Order Boundary Value Problems in Fluid Mechanics and Mathematics

    DEFF Research Database (Denmark)

    Hosseinzadeh, E.; Barari, Amin; Fouladi, F.;

    2011-01-01

    In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed o...

  2. Solution of a singularly perturbed nonstationary fourth-order boundary-value problem

    Energy Technology Data Exchange (ETDEWEB)

    Makarov, V.L.; Guminskii, V.V. [Kiev State Univ. (Ukraine)

    1994-06-05

    A difference scheme is constructed by the method of lines for a nonstationary boundary-value problem for a fourth-order equation in the space coordinate. The uniform convergence with respect to a small parameter, of the solution of the linearization scheme to a solution of the original problem is proven. 8 refs.

  3. Mixed initial-boundary value problem for equations of motion of Kelvin-Voigt fluids

    Science.gov (United States)

    Baranovskii, E. S.

    2016-07-01

    The initial-boundary value problem for equations of motion of Kelvin-Voigt fluids with mixed boundary conditions is studied. The no-slip condition is used on some portion of the boundary, while the impermeability condition and the tangential component of the surface force field are specified on the rest of the boundary. The global-in-time existence of a weak solution is proved. It is shown that the solution is unique and depends continuously on the field of external forces, the field of surface forces, and initial data.

  4. Elliptic boundary value problems for Bessel operators, with applications to anti-de Sitter spacetimes

    CERN Document Server

    Gannot, Oran

    2015-01-01

    This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of anti-de Sitter spacetimes. These problems involve a singular Bessel operator acting in the normal direction. After formulating a Lopatinskii condition, elliptic estimates are established for functions supported near the boundary. A global Fredholm property follows from additional hypotheses in the interior. The results of this paper provide a rigorous framework for the study of quasinormal modes on anti-de Sitter black holes for the full range of boundary conditions considered in the physics literature.

  5. Boundary-value problems for first and second order functional differential inclusions

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2003-03-01

    Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.

  6. Comparison, existence, uniqueness and successive approximations for ordinary and elliptic boundary value problems

    International Nuclear Information System (INIS)

    Bailey, Shampine and Waltman have developed an existence theory for two-point boundary value problems of second-order differential equations whose second members satisfy one-sided Lipshitz conditions. These results suggest that solutions should exist in the following much more general situation: the second member f is bounded by two functions f1, f2, such that the corresponding second-order equations have solutions for two-point boundary value problems. The condition f12 implies that if xsub(i) is a solution of the Picard problem xsub(i)'' = fsub(i)(t, xsub(i)), xsub(i)(a) = A, xsub(i)(b) = B, then x2 and x1 are, respectively, a lower and an upper solution of the Picard problem x'' = f(t,x), x(a) = A, x(a) = A, x(b) = B. Then a well-known result would imply an affirmative answer to our conjecture if x21. The aim of this paper is to provide a comnparison result and to apply it to uniqueness and existence of solutions as well as to the convergence of successive approximations. The argument is so general that it applies to (i) periodic solutions of first-order ordinary differential equations; (ii) periodic solutions and a large class of Sturm-Liouville problems (including Nicoletti boundary value problem) for second-order ordinary differential equations; and (iii) Dirichlet boundary value problems for elliptic equations. (author)

  7. Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

    CERN Document Server

    Zhu, C

    2003-01-01

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.

  8. Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

    International Nuclear Information System (INIS)

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation

  9. Existence and uniqueness of entropy solution to initial boundary value problem for the inviscid Burgers equation

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, Changjiang; Duan, Renjun [Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People' s Republic of China (China)

    2003-02-28

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.

  10. Solvability of a class of second-order quasilinear boundary value problems

    Institute of Scientific and Technical Information of China (English)

    Qing-liu YAO

    2009-01-01

    The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution ff the integration of the limit growth function has an appropriate value.

  11. The use of the Adomian decomposition method for solving multipoint boundary value problems

    International Nuclear Information System (INIS)

    In this paper, a method for solving multipoint boundary value problems is presented. The main idea behind this work is the use of the well-known Adomian decomposition method. In this technique, the solution is found in the form of a rapid convergent series. Using this method, it is possible to obtain the solution of the general form of multipoint boundary value problems. The Adomian decomposition method is not affected by computation round off errors and one is not faced with the necessity of large computer memory and time. To show the efficiency of the developed method, numerical results are presented

  12. Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method

    OpenAIRE

    Zanariah A. Majid; Phang P. See; Mohamed Suleiman

    2011-01-01

    Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs) directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs). This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second ord...

  13. About potential of double layer and boundary value problems for Laplace equation

    International Nuclear Information System (INIS)

    An integral operator raisen by a kernel of the double layer's potential is investigated. The kernel is defined on S (S - two-digit variety of C2 class presented by a boundary of the finite domain in R3). The operator is considered on C(S). Following results are received: the operator's spectrum belongs to [-1,1]; it's eigenvalues and eigenfunctions may be found by Kellog's method; knowledge of the operator's spectrum is enough to construct it's resolvent. These properties permit to point out the determined interation processes, solving boundary value problems for Laplace equation. One of such processes - solving of Roben problem - is generalized on electrostatic problems. 6 refs

  14. Positive Solutions of Singular Boundary Value Problem of Negative Exponent Emden–Fowler Equation

    Indian Academy of Sciences (India)

    Yuxia Wang; Xiyu Liu

    2003-05-01

    This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden–Fowler equation. A necessary and sufficient condition for the existence of [0, 1] positive solutions as well as 1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.

  15. Multiple Positive Solutions of Boundary Value Problems for Systems of Nonlinear Third-Order Differential Equations

    Institute of Scientific and Technical Information of China (English)

    Yaohong LI; Xiaoyan ZHANG

    2013-01-01

    In this paper,we consider boundary value problems for systems of nonlinear thirdorder differential equations.By applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed point theorem,the existence of multiple positive solutions is obtained.As application,we give some examples to demonstrate our results.

  16. Existence of global solutions to free boundary value problems for bipolar Navier-Stokes-Possion systems

    Directory of Open Access Journals (Sweden)

    Jian Liu

    2013-09-01

    Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.

  17. The use of integral information in the solution of a two-point boundary value problem

    Directory of Open Access Journals (Sweden)

    Tomasz Drwięga

    2007-01-01

    Full Text Available We study the worst-case \\(\\varepsilon\\-complexity of a two-point boundary value problem \\(u^{\\prime\\prime}(x=f(xu(x\\, \\(x \\in [0,T]\\, \\(u(0=c\\, \\(u^{\\prime}(T=0\\, where \\(c,T \\in \\mathbb{R}\\ (\\(c \

  18. Positive Solutions for a Class of Coupled System of Singular Three-Point Boundary Value Problems

    OpenAIRE

    Naseer Ahmad Asif; Rahmat Ali Khan

    2009-01-01

    Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type , , , , , , , is established. The nonlinearities , are continuous and may be singular at , and/or , while the parameters , satisfy . An example is also included to show the applicability of our result.

  19. On two-point boundary value problems for second order singular functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Kiguradze, I.; Půža, Bedřich

    2005-01-01

    Roč. 12, 3-4 (2005), s. 271-294. ISSN 0793-1786 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order singular functional differential equation * two-point boundary value problem * solvability Subject RIV: BA - General Mathematics

  20. Positive solutions of a boundary-value problem for second order ordinary differential equations

    Directory of Open Access Journals (Sweden)

    George L. Karakostas

    2000-06-01

    Full Text Available The existence of positive solutions of a two-point boundary value problem for a second order differential equation is investigated. By using indices of convergence of the nonlinearities at zero and at positive infinity, we providea priori upper and lower bounds for the slope of the solutions are also provided.

  1. EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.

  2. Fredholm-type theorem for boundary value problems for systems of nonlinear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    -, May 2014 (2014), s. 113. ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : functional-differential equations * boundary value problems * existence of solutions Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2014 http://www.boundaryvalueproblems.com/content/2014/1/113

  3. Solvability of 2n-order m-point boundary value problem at resonance

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The existence of solutions for the 2n-order m-point boundary value problem at resonance is obtained by using the coincidence degree theory of Mawhin.We give an example to demonstrate our result.The interest is that the nonlinear term may be noncontinuous.

  4. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50. ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili. pdf

  5. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17. ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2014 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  6. POSITIVE SOLUTIONS TO A SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    Liu Yang; Chunfang Shen

    2009-01-01

    By a fixed point theorem in a cone,the existence of at least three positive solutions to a class of second-order multi-point boundary value problem for dynamic equation on time scales with the nonlinear term depends on the first order derivative is studied.

  7. TWO-SCALE FEM FOR ELLIPTIC MIXED BOUNDARY VALUE PROBLEMS WITH SMALL PERIODIC COEFFICIENTS

    Institute of Scientific and Technical Information of China (English)

    Jin-ru Chen; Jun-zhi Cui

    2001-01-01

    In this paper, a dual approximate expression of the exact solution for mixed boundary value problems of second order elliptic PDE with small periodic coefficients is proposed. Meanwhile the error estimate of the dual approximate solution is discussed. Finally, a high-low order coupled two-scale finite element method is given, and its approximate error is analysed.

  8. Analytic solution of an initial-value problem from Stokes flow with free boundary

    OpenAIRE

    Xuming Xie

    2008-01-01

    We study an initial-value problem arising from Stokes flow with free boundary. If the initial data is analytic in disk $mathcal{R}_r$ containing the unit disk, it is proved that unique solution, which is analytic in $mathcal{R}_s$ for $sin (1,r)$, exists locally in time.

  9. Calculating methods of solution of boundary-value problems of mathematical physics

    Energy Technology Data Exchange (ETDEWEB)

    Skopetskii, V.V.; Deineka, V.S.; Sklepovaya, L.I. [Kiev Univ. (Ukraine)] [and others

    1994-11-10

    A new mathematical model is developed for unsteady seepage in a pressure gradient through a compressible foundation of a gravity dam with an antiseepage curtain. High-accuracy discretization algorithms are developed for the corresponding initial boundary-value problem with a discontinuous solution.

  10. PERIODIC BOUNDARY VALUE PROBLEM FOR NONLINEAR INTEGRO-DIFFERENTIAL EQUATION OF MIXED TYPE ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    Yepeng Xing; Qiong Wang; Valery G. Romanovski

    2009-01-01

    We prove several new comparison results and develop the monotone iterative tech-nique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.

  11. Positive solutions of second-order singular boundary value problem with a Laplace-like operator

    Directory of Open Access Journals (Sweden)

    Ge Weigao

    2005-01-01

    Full Text Available By use of the concavity of solution for an associate boundary value problem, existence criteria of positive solutions are given for the Dirichlet BVP , , , where is odd and continuous with , , and may change sign and be singular along a curve in .

  12. Dimension reduction for periodic boundary value problems of functional differential equations

    CERN Document Server

    Sieber, Jan

    2010-01-01

    Periodic boundary-value problems for functional differential equations can be reduced to finite-dimensional algebraic systems of equations. The smoothness assumptions on the right-hand side follow those of the review by Hartung et al. (2006) and are set up such that the result can be applied to differential equations with state-dependent delays.

  13. The second boundary value problem for equations of viscoelastic diffusion in polymers

    CERN Document Server

    Vorotnikov, Dmitry A

    2009-01-01

    The classical approach to diffusion processes is based on Fick's law that the flux is proportional to the concentration gradient. Various phenomena occurring during propagation of penetrating liquids in polymers show that this type of diffusion exhibits anomalous behavior and contradicts the just mentioned law. However, they can be explained in the framework of non-Fickian diffusion theories based on viscoelasticity of polymers. Initial-boundary value problems for viscoelastic diffusion equations have been studied by several authors. Most of the studies are devoted to the Dirichlet BVP (the concentration is given on the boundary of the domain). In this chapter we study the second BVP, i.e. when the normal component of the concentration flux is prescribed on the boundary, which is more realistic in many physical situations. We establish existence of weak solutions to this problem. We suggest some conditions on the coefficients and boundary data under which all the solutions tend to the homogeneous state as tim...

  14. NUMERICAL ANALYSIS OF FORTH-ORDER BOUNDARY VALUE PROBLEMS IN FLUID MECHANICS AND MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Elham Hosseinzadeh

    2010-01-01

    Full Text Available In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed of convergence of this method. It is found that the variational iteration method is a powerful method for solving of the non-linear equations.

  15. Estimates for Deviations from Exact Solutions of Maxwell's Initial Boundary Value Problem

    CERN Document Server

    Pauly, Dirk; Rossi, Tuomo

    2011-01-01

    In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector fields in the space-time cylinder that belongs to the corresponding admissible energy class. For this purpose, we use a method suggested earlier for the wave equation.

  16. Existence of solutions for boundary value problem of fractional order impulsive differential equations systems

    Directory of Open Access Journals (Sweden)

    Weihua JIANG

    2015-04-01

    Full Text Available By defining appropriate linear space and norm, giving the appropriate operator, using the contraction mapping principle and krasnoselskii fixed point theorem respectively, the existence and uniqueness of solutions for boundary value problem of fractional order impulsive differential equations systems are investigated under certain condition that nonlinear term and pulse value are satisfied. An example is given to illustrate that the required conditions can be satisfied.

  17. On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Guotao Wang

    2012-01-01

    Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

  18. Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

    CERN Document Server

    Powers, David L

    2005-01-01

    This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

  19. Estimation of parameters of boundary value problems for linear ordinary differential equations with uncertain data

    CERN Document Server

    Nakonechnyi, Olexandr; Shestopalov, Yury

    2009-01-01

    In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax estimates. We establish that the minimax estimates are expressed via solutions of some systems of differential equations of special type. Similar ...

  20. Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

    KAUST Repository

    Dujardin, G. M.

    2009-08-12

    This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas\\' transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over. © 2009 The Royal Society.

  1. Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations

    Directory of Open Access Journals (Sweden)

    Olivier Sarbach

    2012-08-01

    Full Text Available Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein's theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity. The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein's equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.

  2. A MIXED ELECTRIC BOUNDARY VALUE PROBLEM FOR AN ANTI-PLANE PIEZOELECTRIC CRACK

    Institute of Scientific and Technical Information of China (English)

    ttnAngZlaenyu; KuangZhenbang

    2003-01-01

    The analytical continuation method is adopted to solve a mixed electric boundary value problem for a piezoelectric medium under anti-plane deformation. The crack face is partly conductive and partly impermeable. The results show that the stress intensity factor is identical with the mode III stress intensity factor independent of the conducting length. But the electric field and the electric displacement are dependent on the electric boundary conditions on the crack faces and are singular not only at the crack tips but also at the junctures between the impermeable part and conducting portions.

  3. On the asymptotic of solutions of elliptic boundary value problems in domains with edges

    International Nuclear Information System (INIS)

    Solutions of elliptic boundary value problems in three-dimensional domains with edges may exhibit singularities. The usual procedure to study these singularities is by the application of the classical Mellin transformation or continuous Fourier transformation. In this paper, we show how the asymptotic behavior of solutions of elliptic boundary value problems in general three-dimensional domains with straight edges can be investigated by means of discrete Fourier transformation. We apply this approach to time-harmonic Maxwell's equations and prove that the singular solutions can fully be described in terms of Fourier series. The representation here can easily be used to approximate three-dimensional stress intensity factors associated with edge singularities. (author)

  4. THE HIGHER ASYMPTOTIC EXPANSIONS FINDING FOR BOUNDARY VALUE PROBLEM OF THE ZOM MODEL

    Directory of Open Access Journals (Sweden)

    Kovalenko A. V.

    2013-12-01

    Full Text Available In this article authors propose the asymptotic solution of the boundary value problem modeling the transport of salt ions in the cell electrodialysis desalination unit. The domain of the camera desalting broken into two subdomains: electroneutrality and space charge. Subdomains has own asymptotic expansion. The subdomain of the space charge has unique solvability of the current approach used by the solvability condition of the next approximation

  5. Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Domoshnitsky Alexander

    2009-01-01

    Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.

  6. On a two-point boundary value problem for second order ordinary differential equations with singularities

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Malaguti, L.

    2003-01-01

    Roč. 52, č. 6 (2003), s. 1553-1567. ISSN 0362-546X R&D Projects: GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : second order singular differential equation * two-point boundary value problem * lower and upper functions Subject RIV: BA - General Mathematics Impact factor: 0.354, year: 2003

  7. Monotone methods for solving a boundary value problem of second order discrete system

    Directory of Open Access Journals (Sweden)

    Wang Yuan-Ming

    1999-01-01

    Full Text Available A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

  8. Positive solutions for a nonlinear periodic boundary-value problem with a parameter

    Directory of Open Access Journals (Sweden)

    Jingliang Qiu

    2012-08-01

    Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

  9. Solvability of a three-point nonlinear boundary-value problem

    Directory of Open Access Journals (Sweden)

    Assia Guezane-Lakoud

    2010-09-01

    Full Text Available Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem $$displaylines{ u''+f(t,u= 0,quad 0

  10. The second boundary value problem for equations of viscoelastic diffusion in polymers

    OpenAIRE

    Vorotnikov, Dmitry A.

    2009-01-01

    The classical approach to diffusion processes is based on Fick's law that the flux is proportional to the concentration gradient. Various phenomena occurring during propagation of penetrating liquids in polymers show that this type of diffusion exhibits anomalous behavior and contradicts the just mentioned law. However, they can be explained in the framework of non-Fickian diffusion theories based on viscoelasticity of polymers. Initial-boundary value problems for viscoelastic diffusion equat...

  11. Infinitely many solutions for a fourth-order boundary-value problem

    Directory of Open Access Journals (Sweden)

    Seyyed Mohsen Khalkhali

    2012-09-01

    Full Text Available In this article we consider the existence of infinitely many solutions to the fourth-order boundary-value problem $$displaylines{ u^{iv}+alpha u''+eta(x u=lambda f(x,u+h(u,quad xin]0,1[cr u(0=u(1=0,cr u''(0=u''(1=0,. }$$ Our approach is based on variational methods and critical point theory.

  12. Fractal boundary value problems for integral and differential equations with local fractional operators

    Directory of Open Access Journals (Sweden)

    Yang Xiao-Jun

    2015-01-01

    Full Text Available In the present paper we investigate the fractal boundary value problems for the Fredholm\\Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results. [Projekat Ministarstva nauke Republike Srbije, br. OI 174001, III41006 i br. TI 35006

  13. Extension Theory and Krein-type Resolvent Formulas for Nonsmooth Boundary Value Problems

    DEFF Research Database (Denmark)

    Abels, Helmut; Grubb, Gerd; Wood, Ian Geoffrey

    2014-01-01

    The theory of selfadjoint extensions of symmetric operators, and more generally the theory of extensions of dual pairs, was implemented some years ago for boundary value problems for elliptic operators on smooth bounded domains. Recently, the questions have been taken up again for nonsmooth domai...... analyze resolvents, Poisson solution operators and Dirichlet-to-Neumann operators in this way, also in Sobolev spaces of negative order....

  14. Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

    Institute of Scientific and Technical Information of China (English)

    Yi-rang YUAN; Chang-feng LI; Cheng-shun YANG; Yu-ji HAN

    2009-01-01

    The research of the miscible oil and water displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in the basin evolution as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwind finite difference schemes are proposed. Some techniques, such as the calculus of variations, the change of variables, and the theory of a priori estimates, are used. The optimal order l2-norm estimates are derived for the errors in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method, and the software development.

  15. Computational solution of nonlinear two-point boundary-value problems. [SUPOR Q, in FORTRAN for CDC 6600

    Energy Technology Data Exchange (ETDEWEB)

    Scott, M.R.; Watts, H.A.

    1977-01-01

    A working computer code, called SUPOR Q, which solves quite general nonlinear two-point boundary value problems is described. The nonlinear problem is replaced by a sequence of linear problems by applying quasilinearization (Newton's method) to the nonlinear differential operator. Each linear two-point boundary value problem is solved by an initial-value procedure which combines the well-known technique of superposition with a process called orthonormalization. 3 tables.

  16. Solution matching for a three-point boundary-value problem on atime scale

    Directory of Open Access Journals (Sweden)

    Martin Eggensperger

    2004-07-01

    Full Text Available Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t = f(t, y(t, y^Delta(t, y^{DeltaDelta}(t, quad t in [t_1, t_3] cap mathbb{T},cr y(t_1 = y_1, quad y(t_2 = y_2, quad y(t_3 = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solution satisfying a two-point boundary conditions on $[t_2, t_3] cap mathbb{T}$.

  17. Nonlinear systems of differential inequalities and solvability of certain boundary value problems

    Directory of Open Access Journals (Sweden)

    Tvrdý Milan

    2001-01-01

    Full Text Available In the paper we present some new existence results for nonlinear second order generalized periodic boundary value problems of the form These results are based on the method of lower and upper functions defined as solutions of the system of differential inequalities associated with the problem and their relation to the Leray–Schauder topological degree of the corresponding operator. Our main goal consists in a fairly general definition of these functions as couples from . Some conditions ensuring their existence are indicated, as well.

  18. Solution of Seventh Order Boundary Value Problems by Variation of Parameters Method

    Directory of Open Access Journals (Sweden)

    Muzammal Iftikhar

    2013-01-01

    Full Text Available The induction motor behavior is represented by a fifth order differential equation model. Addition of a torque correction factor to this model accurately reproduces the transient torques and instantaneous real and reactive power flows of the full seventh order differential equation model. The aim of this study is to solve the seventh order boundary value problems and the variation of parameters method is used for this purpose. The approximate solutions of the problems are obtained in terms of rapidly convergent series. Two numerical examples have been given to illustrate the efficiency and implementation of the method.

  19. MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    Sun Jingxian; Liu Yansheng

    2005-01-01

    This paper deals with the singular nonlinear third-order periodic boundary value problem u′″ + ρau = f(t,u), 0 ≤ t ≤ 2π, with u(i)(0) = u(i)(2π), i = 0, 1, 2, where ρ∈ (0, 1/√3) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2π] and employing the fixed point index theory that the problem has at least one or at least two positive solutions.

  20. Lie symmetries and reductions of multi-dimensional boundary value problems of the Stefan type

    International Nuclear Information System (INIS)

    A new definition of Lie invariance for nonlinear multi-dimensional boundary value problems (BVPs) is proposed by the generalization of known definitions to much wider classes of BVPs. The class of (1+3)-dimensional nonlinear BVPs of the Stefan type, modeling the process of melting and evaporation of metals, is studied in detail. Using the definition proposed, the group classification problem for this class of BVPs is solved and some reductions (with physical meaning) to BVPs of lower dimensionality are made. Examples of how to construct exact solutions of the (1+3)-dimensional nonlinear BVP with the correctly specified coefficients are presented. (paper)

  1. Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem

    Science.gov (United States)

    Ramadan, M. A.; Lashien, I. F.; Zahra, W. K.

    2009-04-01

    In this paper, we develop quintic nonpolynomial spline methods for the numerical solution of fourth order two-point boundary value problems. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. The present approach gives better approximations and generalizes all the existing polynomial spline methods up to order four. This approach has less computational cost. Convergence analysis of these methods is discussed. Two numerical examples are included to illustrate the practical usefulness of our methods.

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

    Directory of Open Access Journals (Sweden)

    Olga Lepsky

    2006-05-01

    Full Text Available A homogeneous boundary condition is constructed for the parabolic equation (∂t+I−Δu=f in an arbitrary cylindrical domain Ω×ℝ (Ω⊂ℝn being a bounded domain, I and Δ being the identity operator and the Laplacian which generates an initial-boundary value problem with an explicit formula of the solution u. In the paper, the result is obtained not just for the operator ∂t+I−Δ, but also for an arbitrary parabolic differential operator ∂t+A, where A is an elliptic operator in ℝn of an even order with constant coefficients. As an application, the usual Cauchy-Dirichlet boundary value problem for the homogeneous equation (∂t+I−Δu=0 in Ω×ℝ 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.

  3. Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method

    Directory of Open Access Journals (Sweden)

    Zanariah A. Majid

    2011-01-01

    Full Text Available Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs. This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newton’s method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.

  4. A new efficient recursive technique for solving singular boundary value problems arising in various physical models

    Science.gov (United States)

    Roul, Pradip

    2016-04-01

    The paper deals with a numerical technique for solving nonlinear singular boundary value problems arising in various physical models. First, we convert the original problem to an equivalent integral equation to surmount the singularity and employ afterward the boundary condition to compute the undetermined coefficient. Finally, the integral equation without undetermined coefficient is treated using homotopy perturbation method. The present method is implemented on three physical model examples: i) thermal explosions; ii) steady-state oxygen diffusion in a spherical shell; iii) the equilibrium of the isothermal gas sphere. The results obtained by the present method are compared with that obtained using finite-difference method, B-spline method and a numerical technique based on the direct integration method, and comparison reveals that the proposed method with few solution components produces similar results and the method is computationally efficient than others.

  5. Existence of countably many positive solutions for nth-order m-point boundary-value problems on time scales

    Directory of Open Access Journals (Sweden)

    Zhiyong Wang

    2008-09-01

    Full Text Available In this paper, we study the existence of positive solutions for the nonlinear nth-order with m-point singular boundary-value problem. By using the fixed point index theory and a new fixed point theorem in cones, the existence of countably many positive solutions for a nonlinear singular boundary value problem are obtained.

  6. Probability distribution and the boundary value problem in noncommutative quantum mechanics

    International Nuclear Information System (INIS)

    Full text: Non-commutative quantum mechanics (NCQM) still has some important open questions, such as, for example, the correct definition of the probability density and the consistent formulation of the boundary value problem. The main difficulty relies on the fact that in a non-commutative space the classical notion of point has no operational meaning. Besides that, it is well known that in NCQM the ordinary definition of probability density does not satisfy the continuity equation, thus being physically inadequate to this context. As a consequence, the formulation of the boundary value problem in NCQM is ill-defined, since the confining conditions for a particle trapped in a closed region are often formulated in terms of the properties of the probability density at the boundaries of such a region. In this work we solve both problems in a unified way. We consider a two-dimensional configuration space generated by two non-commutative coordinates satisfying a canonical commutation relation. This non-commutative space is formally equal to the phase space of a quantum particle moving in a line, what suggests an approach based on the Wigner formulation of quantum mechanics. We introduce a quasi-probability distribution function, constructed by means of the Moyal product of functions. By making use of the operation of partial trace we construct a normalizable, positive-definite function. We demonstrate that this function satisfy the continuity equation, so that it can be interpreted as a probability density function, thus providing a physically consistent probabilistic interpretation for NCQM. Even though the probability density contains all the available information about the physical system, it is useful to formulate the boundary value problem in terms of wave functions fulfilling some appropriated differential equation. By making use of harmonic analysis we introduce an auxiliary wave function, which is related to the physical probability density in the same way as

  7. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  8. GLOBAL C1 SOLUTION TO THE INITIAL-BOUNDARY VALUE PROBLEM FOR DIAGONAL HYPERBOLIC SYSTEMS WITH LINEARLY DEGENERATE CHARACTERISTICS

    Institute of Scientific and Technical Information of China (English)

    Li Ta-tsien(李大潜); Peng Yue-Jun

    2003-01-01

    Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.

  9. Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2012-01-01

    Full Text Available In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

  10. Spectral Shifted Jacobi Tau and Collocation Methods for Solving Fifth-Order Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2011-01-01

    Full Text Available We have presented an efficient spectral algorithm based on shifted Jacobi tau method of linear fifth-order two-point boundary value problems (BVPs. An approach that is implementing the shifted Jacobi tau method in combination with the shifted Jacobi collocation technique is introduced for the numerical solution of fifth-order differential equations with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplify the problem. Shifted Jacobi collocation method is developed for solving nonlinear fifth-order BVPs. Numerical examples are performed to show the validity and applicability of the techniques. A comparison has been made with the existing results. The method is easy to implement and gives very accurate results.

  11. Existence of solutions to fractional boundary-value problems with a parameter

    Directory of Open Access Journals (Sweden)

    Ya-Ning Li

    2013-06-01

    Full Text Available This article concerns the existence of solutions to the fractional boundary-value problem $$displaylines{ -frac{d}{dt} ig(frac{1}{2} {}_0D_t^{-eta}+ frac{1}{2}{}_tD_{T}^{-eta}igu'(t=lambda u(t+abla F(t,u(t,quad hbox{a.e. } tin[0,T], cr u(0=0,quad u(T=0. }$$ First for the eigenvalue problem associated with it, we prove that there is a sequence of positive and increasing real eigenvalues; a characterization of the first eigenvalue is also given. Then under different assumptions on the nonlinearity F(t,u, we show the existence of weak solutions of the problem when $lambda$ lies in various intervals. Our main tools are variational methods and critical point theorems.

  12. Solution matching for a three-point boundary-value problem on atime scale

    OpenAIRE

    Martin Eggensperger; Kaufmann, Eric R.; Nickolai Kosmatov

    2004-01-01

    Let $mathbb{T}$ be a time scale such that $t_1, t_2, t_3 in mathbb{T}$. We show the existence of a unique solution for the three-point boundary value problem $$displaylines{ y^{DeltaDeltaDelta}(t) = f(t, y(t), y^Delta(t), y^{DeltaDelta}(t)), quad t in [t_1, t_3] cap mathbb{T},cr y(t_1) = y_1, quad y(t_2) = y_2, quad y(t_3) = y_3,. }$$ We do this by matching a solution to the first equation satisfying a two-point boundary conditions on $[t_1, t_2] cap mathbb{T}$ with a solut...

  13. Optimization of solving the boundary-value problems related to physical geodesy.

    Science.gov (United States)

    Macák, Marek; Mikula, Karol

    2016-04-01

    Our aim is to present different approaches for optimization of solving the boundary-value problem related to physical geodesy in spatial domain. In physical geodesy, efficient numerical methods like the finite element method, boundary element method or finite volume method represent alternatives to classical approaches (e.g. the spherical harmonics). They lead to a solution of the linear system and in this context, we focus on three tasks. First task is to choose the fastest solver with respect to the number of iteration and computational time. The second one is to use parallel techniques (MPI or OpenMP) and the third one is to implement advance method like Multigrid and Domain decomposition. All presented examples deal with the gravity field modelling.

  14. NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    Li Shuhong; Sun Yongping

    2007-01-01

    In this paper, for a second-order three-point boundary value problem u"+f(t,u)=0, 0<t<l,au(0) - bu'(0) = 0, u(1) - αu(η) = 0,where η∈ (0, 1), a, b, α∈ R with a2 + b2 > 0, the existence of its nontrivial solution is studied.The conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

  15. A positive solution for singular discrete boundary value problems with sign-changing nonlinearities

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2006-01-01

    Full Text Available This paper presents new existence results for the singular discrete boundary value problem −Δ2u(k−1=g(k,u(k+λh(k,u(k, k∈[1,T], u(0=0=u(T+1. In particular, our nonlinearity may be singular in its dependent variable and is allowed to change sign.

  16. An Initial and Boundary Value Problem Modeling Fish-like Swimming

    OpenAIRE

    San Martin, Jorge; Scheid, Jean-François; Takahashi, Takéo; Tucsnak, Marius

    2008-01-01

    In this paper we consider an initial and boundary value problem modeling the self-propelled motion of solids in a bi-dimensional viscous incompressible fluid. The self-propelling mechanism, consisting in appropriate deformations of the solids, is a simplified model for the propulsion mechanism of fish-like swimmers. The governing equations are composed of the Navier-Stokes equations for the fluid, coupled to Newton's laws for the solids. Since we consider the case in which the fluid-solid sys...

  17. Solvability on boundary-value problems of elasticity of three-dimensional quasicrystals

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    Weak solution (or generalized solution) for the boundary-value problems of partial differential equations of elasticity of 3D (three-dimensional) quasicrystals is given,in which the matrix expression is used. In terms of Korn inequality and theory of function space, we prove the uniqueness of the weak solution. This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals, and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students.

  18. A NEW EFFICIENT METHOD TO BOUNDARY VALUE PROBLEM FOR BALLISTIC ROCKET GUIDANCE

    Institute of Scientific and Technical Information of China (English)

    2005-01-01

    The exploitation of rocket guidance technology on the basis of the guidance law of Space Shuttle and Pegasus rocket was performed. A new efficient method of numerical iteration solution to the boundary value problem was put forward. The numerical simulation results have shown that the method features good performances of stability, robustness, high precision, and algebraic formulas in real computation. By virtue of modern DSP (digital signal processor) high speed chip technology, the algorithm can be used in real time and can adapt to the requirements of the big primary bias of rocket guidance.

  19. Positive solutions of singular fourth-order boundary-value problems

    Directory of Open Access Journals (Sweden)

    Yujun Cui

    2006-03-01

    Full Text Available In this paper, we present necessary and sufficient conditions for the existence of positive $C^3[0,1]cap C^4(0,1$ solutions for the singular boundary-value problem $$displaylines{ x''''(t=p(tf(x(t,quad tin(0,1;cr x(0=x(1=x'(0=x'(1=0, }$$ where $f(x$ is either superlinear or sublinear, $p:(0,1o [0,+infty$ may be singular at both ends $t=0$ and $t=1$. For this goal, we use fixed-point index results.

  20. Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem

    International Nuclear Information System (INIS)

    In this paper we present two equilibrium solvers for axisymmetrical toroidal configurations, both based on the expansion in poloidal angle method. The first one has been conceived as a two-point boundary value solver in a system of coordinates with straight field lines, while the second one uses a well-conditioned Cauchy formulation of the problem in a general curvilinear coordinate system. In order to check the capability of our moment methods to describe equilibrium accurately, a comparison of the moment solutions with analytical solutions obtained for a Solov'ev equilibrium has been performed. (author)

  1. The Fourth Main Boundary Value Problem of Dynamics of Thermo-resiliency’s Momentum Theory

    Directory of Open Access Journals (Sweden)

    Merab Aghniashvili

    2014-08-01

    Full Text Available In the paper is presented the fourth main boundary value problem of Dynamics of Thermo-resiliency’s Momentum theory. The problem states to find in the cylinder D_l the regular solution of the system: M(∂_x U-νχθ-χ^0 (∂^2 U/(∂t^2 =H, ∆θ-1/ϑ ∂θ/∂t-η ∂/∂t div u=H_7, which satisfies the initial conditions: 〖∀x∈D: lim〗┬(t→0⁡〖U(x,t=φ^((0 (x,〗 lim┬(t→0⁡〖θ(x,t=φ_7^((0 (x, lim┬(t→0 ∂U(x,t/∂t=φ^((1 〗 (x and the boundary conditions: 〖∀(x,t∈S_l:lim┬(D∋x→y∈S〗⁡〖PU=f, 〗 lim┬(D∋x→y∈S {θ}_S^±=f_7. The uniqueness theorem of the solution is proved for this problem.

  2. Positive Solutions for Second-Order m-Point Boundary Value Problems on Time Scales

    Institute of Scientific and Technical Information of China (English)

    Wan Tong LI; Hong Rui SUN

    2006-01-01

    Let T be a time scale such that 0, T ∈ T. By means of the Schauder fixed point theorem and analysis method, we establish some existence criteria for positive solutions of the m-point boundary value problem on time scaleswhere a ∈ Cld((0, T),[0,∞)), f ∈ Cld([0, ∞) × [0, ∞),[0, ∞)), β,γ∈ [0, ∞), ξi ∈ (0, ρ(T)), b, ai ∈(0, ∞) (for i = 1,..., m - 2) are given constants satisfying some suitable hypotheses. We show that this problem has at least one positive solution for sufficiently small b > 0 and no solution for sufficiently large b. Our results are new even for the corresponding differential equation (T= R) and difference equation (T = Z).

  3. EXISTENCE AND MULTIPLE EXISTENCE OF POSITIVE SOLUTIONS TO SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM ON TIME SCALES

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    By different fixed point theorems in cones, sufficient conditions for the existence and multiple existence of positive solutions to a class of second-order multi-point boundary value problem for dynamic equation on time scales are obtained.

  4. Coarse projective kMC integration: forward/reverse initial and boundary value problems

    International Nuclear Information System (INIS)

    In 'equation-free' multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various low-order moments of the distributions evolved through the microscopic model. We consider the problem of integrating these unavailable equations by acting directly on kinetic Monte Carlo microscopic simulators, thus circumventing their derivation in closed form. In particular, we use projective multi-step integration to solve the coarse initial value problem forward in time as well as backward in time (under certain conditions). Macroscopic trajectories are thus traced back to unstable, source-type, and even sometimes saddle-like stationary points, even though the microscopic simulator only evolves forward in time. We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of 'coarse limit cycles' of the macroscopic behavior, and the approximation of their stability through estimates of the leading 'coarse Floquet multipliers'

  5. New formulations on the finite element method for boundary value problems with internal/external boundary layers

    International Nuclear Information System (INIS)

    New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

  6. Collisional plasma transport: two-dimensional scalar formulation of the initial boundary value problem and quasi one-dimensional models

    International Nuclear Information System (INIS)

    The collisional plasma transport problem is formulated as an initial boundary value problem for general characteristic boundary conditions. Starting from the full set of hydrodynamic and electrodynamic equations an expansion in the electron-ion mass ratio together with a multiple timescale method yields simplified equations on each timescale. On timescales where many collisions have taken place for the simplified equations the initial boundary value problem is formulated. Through the introduction of potentials a two-dimensional scalar formulation in terms of quasi-linear integro-differential equations of second order for a domain consisting of plasma and vacuum sub-domains is obtained. (Auth.)

  7. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

    OpenAIRE

    Balint AgnetaMaria; Balint Stefan

    2008-01-01

    Abstract The boundary value problem , , , , and is strictly decreasing on , is considered. Here, are constants having the following properties: are strictly positive and . Necessary or sufficient conditions are given in terms of for the existence of concave solutions of the above nonlinear boundary value problem (NLBVP). Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by e...

  8. ASYMPTOTICS OF INITIAL BOUNDARY VALUE PROBLEMS OF BIPOLAR HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

    Institute of Scientific and Technical Information of China (English)

    Ju Qiangchang

    2004-01-01

    In this paper, we study the asymptotic behavior of the solutions to the bipolar hydrodynamic model with Dirichlet boundary conditions. It is shown that the initial boundary problem of the model admits a global smooth solution which decays to the steady state exponentially fast.

  9. Numerical continuation methods for dynamical systems path following and boundary value problems

    CERN Document Server

    Krauskopf, Bernd; Galan-Vioque, Jorge

    2007-01-01

    Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel''s 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects ...

  10. Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems

    Energy Technology Data Exchange (ETDEWEB)

    Massoudi, M.C.; Tran, P.X.

    2006-01-01

    We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.

  11. Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Thanin Sitthiwirattham

    2012-01-01

    Full Text Available By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problem Δ2u(t-1+a(tf(u(t=0, t∈{1,2,…,T}, u(0=β∑s=1ηu(s, u(T+1=α∑s=1ηu(s, where f is continuous, T≥3 is a fixed positive integer, η∈{1,2,...,T-1}, 0<α<(2T+2/η(η+1, 0<β<(2T+2-αη(η+1/η(2T-η+1, and Δu(t-1=u(t-u(t-1. We show the existence of at least one positive solution if f is either superlinear or sublinear.

  12. A symmetric solution of a multipoint boundary value problem at resonance

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available We apply a coincidence degree theorem of Mawhin to show the existence of at least one symmetric solution of the nonlinear second-order multipoint boundary value problem u ″ ( t = f ( t , u ( t , | u ′ ( t | , t ∈ ( 0 , 1 , u ( 0 = ∑ i = 1 n μ i u ( ξ i , u ( 1 − t = u ( t , t ∈ ( 0 , 1 ] , where 0 < ξ 1 < ξ 2 < … ≤ ξ n 1 / 2 , ∑ i = 1 n μ i = 1 , f : [ 0 , 1 ] × ℝ 2 → ℝ with f ( t , x , y = f ( 1 − t , x , y , ( t , x , y ∈ [ 0 , 1 ] × ℝ 2 , satisfying the Carathéodory conditions.

  13. Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions

    Czech Academy of Sciences Publication Activity Database

    Babuška, I.; Chleboun, Jan

    2002-01-01

    Roč. 71, č. 240 (2002), s. 1339-1370. ISSN 0025-5718 R&D Projects: GA ČR GA201/98/0528 Keywords : Neumann boundary value problem * uncertain boundary * stability Subject RIV: BA - General Mathematics Impact factor: 1.015, year: 2002

  14. An initial-boundary value problem in a strip for a two-dimensional equation of Zakharov-Kuznetsov type

    OpenAIRE

    Faminskii, Andrei V.

    2013-01-01

    An initial-boundary value problem in a strip with homogeneous Diriclet boundary conditions for two-dimensional generalized Zakharov-Kuznetsov equation is considered. In particular, dissipative and absorbing degenerate terms can be supplemented to the original Zakharov-Kuznetsov equation. Results on global existence, uniqueness and long-time decay of weak silutions are established.

  15. Advances in the study of boundary value problems for nonlinear integrable PDEs

    International Nuclear Information System (INIS)

    In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the ‘separation of variables’ philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance. (invited article)

  16. Interior and exterior solutions for boundary value problems in composite elastic and viscous media

    Directory of Open Access Journals (Sweden)

    R. P. Kanwal

    1985-06-01

    Full Text Available We present the solutions for the boundary value problems of elasticity when a homogeneous and isotropic solid of an arbitrary shape is embedded in an infinite homogeneous isotropic medium of different properties. The solutions are obtained inside both the guest and host media by an integral equation technique. The boundaries considered are an oblong, a triaxial ellipsoid and an elliptic cyclinder of a finite height and their limiting configurations in two and three dimensions. The exact interior and exterior solutions for an ellipsoidal inclusion and its limiting configurations are presented when the infinite host medium is subjected to a uniform strain. In the case of an oblong or an elliptic cylinder of finite height the solutions are approximate. Next, we present the formula for the energy stored in the infinite host medium due to the presence of an arbitrary symmetrical void in it. This formula is evaluated for the special case of a spherical void. Finally, we analyse the change of shape of a viscous incompressible ellipsoidal region embedded in a slowly deforming fluid of a different viscosity. Two interesting limiting cases are discussed in detail.

  17. Advances in the study of boundary value problems for nonlinear integrable PDEs

    Science.gov (United States)

    Pelloni, Beatrice

    2015-02-01

    In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the ‘separation of variables’ philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance.

  18. Existence of 2m-1 Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

    Directory of Open Access Journals (Sweden)

    Yanmei Sun

    2012-01-01

    Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

  19. Positive solutions to boundary-value problems of p-Laplacian fractional differential equations with a parameter in the boundary

    Directory of Open Access Journals (Sweden)

    Zhenlai Han

    2012-11-01

    Full Text Available In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with $p$-Laplacian operator $$displaylines{ D_{0+}^eta(phi_p(D_{0+}^alpha u(t+a(tf(u=0, quad 01$, $phi_p^{-1}=phi_q$, $1/p+1/q=1$, $0leqslantgamma<1$, $0leqslantxileqslant1$, $lambda>0$ is a parameter, $a:(0,1o [0,+infty$ and $f:[0,+inftyo[0,+infty$ are continuous. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence results for positive solutions, in terms of the parameter $lambda$ are obtained. The uniqueness of positive solution on the parameter $lambda$ is also studied. Some examples are presented to illustrate the main results.

  20. Boundary value problems of finite elasticity local theorems on existence, uniqueness, and analytic dependence on data

    CERN Document Server

    Valent, Tullio

    1988-01-01

    In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b]...

  1. Iteration scheme for the multiparameter nonlinear boundary value problem with the additional conditions and its application to some field models

    International Nuclear Information System (INIS)

    The iterative scheme based on the combination of Continuous analogue of the Newton's method and Continuation method was developed for the solving a boundary value problem together with an additional condition. The accuracy was investigated numerically. The suggested method was applied for the numerical investigation of the equations of the solvated electron problem, of some bielectron problem and one QCD problem with an increasing potential. 10 refs.; 6 figs.; 2 tabs

  2. Existence of Positive Solutions for Second-Order m-Point Boundary Value Problems on Time Scales

    Institute of Scientific and Technical Information of China (English)

    Pei-guang Wang; Ying Wang

    2006-01-01

    This paper investigates the existence of positive solutions of the m-point boundary value problem for second-order dynamic equations on time scales, and obtain the result that the problem has at least one positive solution by using functional-type cone expansion-compression fixed point theorem.

  3. THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHR(O)DINGER-POISSON EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this article, the author studies the initial-(Dirichlet) boundary problem for a high-field version of the Schr(o)dinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schrodinger equations on the unit cube. A global existence and uniqueness is established for a solution to this problem.

  4. On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum

    OpenAIRE

    Boulton, Lyonell; Levitin, Michael; Marletta, Marco

    2010-01-01

    In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.

  5. Positive Solutions to m-point Boundary Value Problem of Fractional Differential Equation

    Institute of Scientific and Technical Information of China (English)

    Yuan-sheng TIAN

    2013-01-01

    In this paper,we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations:{Dqu(t)+f(t,u(t))=0,0<t<1,u(0) =0,u(1)=m-2Σ i=1μiDpu(t) |t=ξi,where q∈R,1<q≤2,0<ξ1<ξ2<…<ξm-2≤1/2,μ∈[0,+∞) and p =q-1/ 2,Γ(q)m-2 Σ i=1μiξi q-1/2 < Γ(q+1/2),Dq is the standard Riemann-Liouville differentiation,and f∈C([0,1] × [0,+∞),[0,+∞)).By using the Leggett-Williams fixed point theorem on a convex cone,some multiplicity results of positive solutions are obtained.

  6. Existence of solutions to boundary value problems arising from the fractional advection dispersion equation

    Directory of Open Access Journals (Sweden)

    Lingju Kong

    2013-04-01

    Full Text Available We study the existence of multiple solutions to the boundary value problem $$displaylines{ frac{d}{dt}Big(frac12{}_0D_t^{-eta}(u'(t+frac12{}_tD_T^{-eta}(u'(t Big+lambda abla F(t,u(t=0,quad tin [0,T],cr u(0=u(T=0, }$$ where $T>0$, $lambda>0$ is a parameter, $0leqeta<1$, ${}_0D_t^{-eta}$ and ${}_tD_T^{-eta}$ are, respectively, the left and right Riemann-Liouville fractional integrals of order $eta$, $F: [0,T]imesmathbb{R}^Nomathbb{R}$ is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when $eta=0$. Examples are provided to illustrate the applicability of our results.

  7. On the Initial-Boundary-Value Problem for the Time-Fractional Diffusion Equation on the Real Positive Semiaxis

    Directory of Open Access Journals (Sweden)

    D. Goos

    2015-01-01

    Full Text Available We consider the time-fractional derivative in the Caputo sense of order α∈(0, 1. Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in R+, two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when α↗1 of the respective solutions is analyzed, recovering the solutions of the classical boundary-value problems when α = 1, and the fractional diffusion equation becomes the heat equation.

  8. 跨共振的周期-积分边值问题%Periodic-Integral Boundary Value Problems across Resonance

    Institute of Scientific and Technical Information of China (English)

    宋新; 杨雪

    2011-01-01

    研究二阶微分方程周期-积分边值问题,应用最优控制理论给出了跨多个共振情形下的二阶微分方程周期-积分边值问题唯一可解的最优条件.%The periodic-integral boundary value problems for second order differential equations were considered. On the basis of optimal control theory method, we gave an optimal condition of the unique solvability to the periodic-integral boundary value problems for second order differential equations across multiple resonance.

  9. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

    Directory of Open Access Journals (Sweden)

    Balint AgnetaMaria

    2008-01-01

    Full Text Available Abstract The boundary value problem , , , , and is strictly decreasing on , is considered. Here, are constants having the following properties: are strictly positive and . Necessary or sufficient conditions are given in terms of for the existence of concave solutions of the above nonlinear boundary value problem (NLBVP. Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG method. With this aim, this study was undertaken.

  10. Two-point boundary value problems and exact controllability for several kinds of linear and nonlinear wave equations

    International Nuclear Information System (INIS)

    All articles must In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations arising from physics and geometry, we prove the existence of smooth solutions of the two-point boundary value problems and show the global exact controllability of these wave equations. In particular, we investigate the two-point boundary value problem for one-dimensional wave equation defined on a closed curve and prove the existence of smooth solution which implies the exact controllability of this kind of wave equation. Furthermore, based on this, we study the two-point boundary value problems for the wave equation defined on a strip with Dirichlet or Neumann boundary conditions and show that the equation still possesses the exact controllability in these cases. Finally, as an application, we introduce the hyperbolic curvature flow and obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves.

  11. Boundary value problems of the linearized non-homogeneous Navier-Stokes equations for the axisymmetrical slow motion

    International Nuclear Information System (INIS)

    The boundary value problem of axisymmetrical slow motion of viscous incompressible fluid in the upper half-space or in the whole space surrounding a fixed infinite circular cylinder is considered. The solution of the linearized non-homogeneous Navier-Stokes equations is obtained in each case in quadratures by using Abel integral equations, which transform the axisymmetrical problem to solvable two dimensional plane problem. (author)

  12. Existence of positive solutions for nonlocal second-order boundary value problem with variable parameter in Banach spaces

    Directory of Open Access Journals (Sweden)

    Zhang Peiguo

    2011-01-01

    Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.

  13. Robin boundary value problems for elliptic operational differential equations with variable coefficients

    Directory of Open Access Journals (Sweden)

    Rabah Haoua

    2015-04-01

    Full Text Available In this article we give some new results on abstract second-order differential equations of elliptic type with variable operator coefficients and general Robin boundary conditions, in the framework of Holder spaces. We assume that the family of variable coefficients verify the well known Labbas-Terreni assumption used in the sum theory. We use Dunford calculus, interpolation spaces and the semigroup theory to obtain existence, uniqueness and maximal regularity results for the solution of the problem.

  14. Positive Solutions for a Class of Fourth-Order -Laplacian Boundary Value Problem Involving Integral Conditions

    OpenAIRE

    Yan Sun

    2015-01-01

    Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples ...

  15. Characteristic finite difference method and application for moving boundary value problem of coupled system

    Institute of Scientific and Technical Information of China (English)

    YUAN Yi-rang; LI Chang-feng; YANG Cheng-shun; HAN Yu-ji

    2008-01-01

    The coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. A kind of characteristic finite difference schemes is put forward, from which optimal order estimates in l2 norm are derived for the error in the approximate solutions. The research is important both theoretically and practically for the model analysis in the field, the model numerical method and software development.

  16. Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order -Point Boundary Value Problem

    Directory of Open Access Journals (Sweden)

    Lv Xuezhe

    2010-01-01

    Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.

  17. Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators

    Directory of Open Access Journals (Sweden)

    M. Venkatesulu

    1995-12-01

    Full Text Available An algorithm for the computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators is presented and two examples from the studies of acoustic waveguides in ocean and transverse vibrations in nonhomogeneous strings are discussed.

  18. On nonnegative solutions of a certain nonlocal boundary value problem for second order linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Vodstrčil, Petr

    2004-01-01

    Roč. 11, č. 3 (2004), s. 583-602. ISSN 1072-947X Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equation * nonnegative solution * three-point boundary value problem Subject RIV: BA - General Mathematics

  19. Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

    Directory of Open Access Journals (Sweden)

    Chatthai Thaiprayoon

    2014-01-01

    Full Text Available By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

  20. GLOBAL WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    GUO Fei

    2007-01-01

    In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D={(t,x)| t≥O,x≥O}.Under the assumption that the source term satisfies the matching condition,a sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

  1. Existence of solutions for two-point boundary-value problems with singular differential equations of variable order

    Directory of Open Access Journals (Sweden)

    Shuqin Zhang

    2013-11-01

    Full Text Available In this work, we show the existence of a solution for a two-point boundary-value problem having a singular differential equation of variable order. We use some analysis techniques and the Arzela-Ascoli theorem, and then illustrate our results with examples.

  2. Numerical solution of boundary value problems for stochastic differential equations on the basis of the Gibbs sampler

    OpenAIRE

    Prigarin, Sergej M.; Winkler, Gerhard

    2003-01-01

    To solve boundary value problems for linear systems of stochastic differential equations we propose and justify a numerical method based on the Gibbs sampler. In contrast to the technique which yields for linear systems an "exact" numerical solution, the proposed method is simpler to generalize for stochastic partial differential equations and nonlinear systems. Such generalizations are discussed as well.

  3. CALCULUS OF VARIATIONS WITH DIRICHLET BOUNDARY VALUE PROBLEM FOR PERTURBED SECOND-ORDER DIFFERENTIAL EQUATIONS ON A HALF-LINE

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    Dirichlet boundary value problems for perturbed second-order differential equations on a half line are investigated in this paper. The methods mainly depend on the calculus of variations to the classical functionals. Sufficient conditions are obtained for the existence of the solutions.

  4. EXISTENCE OF POSITIVE SOLUTION TO TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.

  5. HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    王同科

    2002-01-01

    In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs fromthe high order generalized difference methods. It is proved that the method has optimal order er-ror estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

  6. Elliptic boundary value problems on corner domains smoothness and asymptotics of solutions

    CERN Document Server

    Dauge, Monique

    1988-01-01

    This research monograph focusses on a large class of variational elliptic problems with mixed boundary conditions on domains with various corner singularities, edges, polyhedral vertices, cracks, slits. In a natural functional framework (ordinary Sobolev Hilbert spaces) Fredholm and semi-Fredholm properties of induced operators are completely characterized. By specially choosing the classes of operators and domains and the functional spaces used, precise and general results may be obtained on the smoothness and asymptotics of solutions. A new type of characteristic condition is introduced which involves the spectrum of associated operator pencils and some ideals of polynomials satisfying some boundary conditions on cones. The methods involve many perturbation arguments and a new use of Mellin transform. Basic knowledge about BVP on smooth domains in Sobolev spaces is the main prerequisite to the understanding of this book. Readers interested in the general theory of corner domains will find here a new basic t...

  7. ON UNBOUNDED OPTIMAL CONTROLS IN COEFFICIENTS FOR ILL-POSED ELLIPTIC DIRICHLET BOUNDARY VALUE PROBLEMS

    Directory of Open Access Journals (Sweden)

    Т. Horsin

    2014-01-01

    Full Text Available We consider an optimal control problem associated to Dirichlet boundary valueproblem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coecients A(x of such system as a control in L1(Ω;RN RN. One of the important features of the admissible controls is the fact that the coecient matrices A(x are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part Asym = (A + At=2 may vanish in Ω.

  8. An approach to the scalar boundary value problem of physical geodesy by means of Nash-Hörmander Theorem

    OpenAIRE

    Otero Juez, Jesús

    1987-01-01

    In this paper he Nahs-Hörmander theorem is used in order to get a new exsitence and uniqueness result for the Scalar Boundary Value Problem of Physical Geodesy. The existence is proved for C[...] neighbourhood of admisible telluroids while the uniqueness is only verified in a C[...] neighbourhood, the results being similar to those ones obtained by Hörmander in his study of the Molodensky's problem.

  9. Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

    Directory of Open Access Journals (Sweden)

    Gai Gongqi

    2011-01-01

    Full Text Available Abstract This article studies the boundary value problems for the third-order nonlinear singular difference equations Δ 3 u ( i - 2 + λ a ( i f ( i , u ( i = 0 , i ∈ [ 2 , T + 2 ] , satisfying five kinds of different boundary value conditions. This article shows the existence of positive solutions for positone and semi-positone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. MSC [2008]: 34B15; 39A10.

  10. Godunov's method for initial-boundary value problem of scalar conservation laws%单个守恒律方程初边值问题的Godunov算法

    Institute of Scientific and Technical Information of China (English)

    林贵成; 盛万成

    2008-01-01

    This paper is concerned with Godunov's scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov's scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.

  11. Multiple solutions for systems of multi-point boundary value problems

    Directory of Open Access Journals (Sweden)

    John R. Graef

    2013-01-01

    Full Text Available In this paper, we establish the existence of at least three solutions of the multi-point boundary value system \\[\\left\\{\\begin{array}{ll} -(\\phi_{p_i}(u'_{i}'=\\lambda F_{u_{i}}(x,u_{1},\\ldots,u_{n},\\ t\\in(0,1,\\\\ u_{i}(0=\\sum_{j=1}^m a_ju_i(x_j,\\ u_{i}(1=\\sum_{j=1}^m b_ju_i(x_j, \\end{array}\\right. i=1,\\ldots,n.\\] The approaches used are based on variational methods and critical point theory.

  12. Trigonometric splines in problems of constructing approximate solutions of the first boundary value problems for ordinary differential equations of second order

    Directory of Open Access Journals (Sweden)

    В.П. Денисюк

    2009-02-01

    Full Text Available  The method of application of trigonometric splines is considered for the problems of construction of the approximate solution of the first boundary value problem for ordinary differential equations of the second orders with variable coefficients. By the method of collocations indefinite coefficients are determined.

  13. THE UPWIND FINITE DIFFERENCE METHOD FOR MOVING BOUNDARY VALUE PROBLEM OF COUPLED SYSTEM

    Institute of Scientific and Technical Information of China (English)

    Yuan Yirang

    2011-01-01

    Coupled system of multilayer dynamics of fluids in porous media is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. The upwind finite difference schemes applicable to parallel arith- metic are put forward and two-dimensional and three-dimensional schemes are used to form a complete set. Some techniques, such as change of variables, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order dif- ference operators and prior estimates, are adopted. The estimates in 12 norm are derived to determine the error in the approximate solution. This method was already applied to the numerical simulation of migration-accumulation of oil resources.

  14. Influence of the course boundary value problem on length scale parmeters for second-gradient continuum theories

    Energy Technology Data Exchange (ETDEWEB)

    Luscher, Darby J [Los Alamos National Laboratory; Bronkhorst, Curt A [Los Alamos National Laboratory; Mc Dowell, David L [GEORGIA TECH

    2010-12-20

    All nonlocal continuum descriptions of inelastic material response involve length scale parameters that either directly or implicitly quantify the physical dimensions of a neighborhood of response which influences the behavior at a particular point. The second-gradient continuum theories such as those developed by Germain, Toupin and Mindlin, and Eringen, and giving rise to strain-gradient plasticity, is becoming a common coarse-scale basis for homogenization of material response that respects the non local nature of heterogeneous material response. Ideally, the length scale parameters involved in such homogenization would be intrinsically associated with dominant aspects of the microstructure. However, these parameters, at least in some cases, are inextricably linked to the details of the coarse scale boundary value problem. Accordingly, they cannot be viewed as pure constitutive parameters. An example problem of multiscale homogenization is presented to underscore the dependence of second-gradient length scale parameters on the coarse scale boundary value problem, namely the multiscale response of an idealized porous microstructure. The fine scale (microstructure) comprises elastic perfectly plastic matrix with a periodic array of circular voids. This fine scale description of the problem is identical for two separate classes of coarse scale boundary value problem, viz. an extruded channel subject to compression and eventually developing plastic shear bands and a thin layer of material with larger (coarse scale) elliptical voids subject to shear deformation. Implications of the relationship between length scale parameters and the details of the coarse scale boundary value problem are discussed and ideas to ascertain such length parameters from evolving response fields are presented.

  15. The mixed boundary value problem, Krein resolvent formulas and spectral asymptotic estimates

    DEFF Research Database (Denmark)

    Grubb, Gerd

    2011-01-01

    For a second-order symmetric strongly elliptic operator A on a smooth bounded open set in Rn, the mixed problem is defined by a Neumann-type condition on a part Σ+ of the boundary and a Dirichlet condition on the other part Σ−. We show a Kreĭn resolvent formula, where the difference between its...... resolvent and the Dirichlet resolvent is expressed in terms of operators acting on Sobolev spaces over Σ+. This is used to obtain a new Weyl-type spectral asymptotics formula for the resolvent difference (where upper estimates were known before), namely sjj2/(n−1)→C0,+2/(n−1), where C0,+ is proportional to...

  16. Boundary value problem for one-dimensional fractional differential advection-dispersion equation

    Directory of Open Access Journals (Sweden)

    Khasambiev Mokhammad Vakhaevich

    2014-07-01

    Full Text Available An equation commonly used to describe solute transport in aquifers has attracted more attention in recent years. After a formal study of some aspects of the advection-diffusion equation, basically from the mathematical point of view with the solution of a differential equation with fractional derivative, the main interest to this problem shifted onto physical aspects of the dynamical system, such as the total energy and the dynamical response. In this regard it should be pointed out that the interaction with environment is expressed in terms of stochastic arrow of time. This allows one also to reach a progress in one more issue. Formerly the equation of advection-diffusion was not obtained from any physical principles. However, mainly the success concerns linear fractional systems. In fact, there are many cases in which linear treatments are not sufficient. The more general systems described by nonlinear fractional differential equations have not been studied enough. The ordinary calculus brings out clearly that essentially new phenomena occur in nonlinear systems, which generally cannot occur in linear systems. Due to vast range of application of the fractional advection-dispersion equation, a lot of work has been done to find numerical solution and fundamental solution of this equation. The research on the analytical solution of initial-boundary problem for space-fractional advection-dispersion equation is relatively new and is still at an early stage of development. In this paper, we will take use of the method of variable separation to solve space-fractional advection-dispersion equation with initial boundary data.

  17. Mean-field games and two-point boundary value problems

    OpenAIRE

    Mylvaganam, T.; Bauso, D.; Astolfi, A.

    2015-01-01

    © 2014 IEEE. A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equa...

  18. Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE

    CERN Document Server

    Henkin, Gennadi M

    2011-01-01

    Let $G\\subset \\C P^n$ be a linearly convex compact with smooth boundary, $D={\\C}P^n\\setminus G$, and let $D^* \\subset (\\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of dimension $d$ we construct an explicit inversion formula for the complex Radon transform $R_V:\\ H^{d,d-1}(V\\cap D)\\to H^{1,0}(D^*)$, and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on $D^*$.

  19. On a Boundary-Value Problem for One Class of Differential Equations of the Fourth Order with Operator Coefficients

    CERN Document Server

    Aliev, A R

    2011-01-01

    The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and unique solvability of the boundary-value problem is proved, and the solvability conditions are expressed in terms of the operator coefficients of the equation. Estimations of the norms of the operators of intermediate derivatives, closely connected with the solvability conditions, have been carried out. The connection between the exponent of the weight and the lower border of the spectrum of the main operator, participating in the equation, is determined in the results of the paper.

  20. Positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations in ordered Banach spaces

    OpenAIRE

    Liang Yue; Yang He

    2011-01-01

    Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...

  1. The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems

    OpenAIRE

    Navnit Jha; R. K. Mohanty; Vinod Chauhan

    2014-01-01

    An efficient algorithm for the numerical solution of higher (even) orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method h...

  2. The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends

    CERN Document Server

    Cardone, G; Nazarov, S A

    2009-01-01

    A simple sufficient condition on curved end of a straight cylinder is found that provides a localization of the principal eigenfunction of the mixed boundary value for the Laplace operator with the Dirichlet conditions on the lateral side. Namely, the eigenfunction concentrates in the vicinity of the ends and decays exponentially in the interior. Similar effects are observed in the Dirichlet and Neumann problems, too.

  3. Bifurcations of spatially inhomogeneous solutions in two boundary value Problems for the generalized Kuramoto-Sivashinsky equation

    International Nuclear Information System (INIS)

    Two boundary value problems for the generalized Kuramoto-Sivashinsky equation have been considered with the use of the theories of invariant manifolds, normal forms and the asymptotic methods. The equation in question describes the ripple topography induced by ion bombardment. This topography can appear when the homogeneous equilibrium states change stability. The possibility of emerging two- or three-dimensional local attractors containing unstable solutions has been shown

  4. A New Algorithm Based on the Homotopy Perturbation Method For a Class of Singularly Perturbed Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    A New Algorithm Based on the Homotopy Perturbation Method For a Class of Singularly Perturbed Boundary Value Problems

    2013-12-01

    Full Text Available . In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and efficiency of the proposed method.

  5. Mathematical apparatus for boundary value problems in gravity field studies and the geometry of the solution domain

    Science.gov (United States)

    Holota, Petr; Nesvadba, Otakar

    2014-05-01

    In geodesy mathematical techniques for gravity field studies that rest on the concept of the so-called classical solution of boundary value problems, have a rather traditional position. Nevertheless, the range of the tools for treating problems in this field is much wider. For instance the concept of the weak solution met with a considerable attention. From this point of view the approach is associated with constructing the respective integral kernels or Green's function in case we consider the classical solution concept or with the choice and constructing basis functions in case we are lucking for the weak solution of the problem. Within the tools considered we discuss also the use of reproducing kernels. In both the cases (classical or weak) the construction of the apparatus above represents and important technical step. It is not elementary, but for a number of fundamental boundary value problems the solution is known, in particular in the case of a spherical solution domain. The sphere, however, is rather far from the real shape of the Earth, which is interpreted here in terms of a functional analytic norm. The distance has a negative effect on any attempt to reach the solution of the boundary value problems considered (and to bridge the departure of the Earth's surface from the sphere) by an iteration procedure based on a successive application of a solution technique developed for the spherical boundary. From this point of view the construction of the integral kernels and basis functions for an oblate ellipsoid of revolution means a step closer towards reality. In this contribution we on the one hand give an overview of the results already achieved and subsequently develop the topic. The summation of series of ellipsoidal harmonics is one of the key problems in this connection. Hypergeometric functions and series are applied too. We also show where the use of Legendre elliptic integrals adds to the solution of the problem. It is interesting that they do not

  6. Three-Point Boundary Value Problems of Nonlinear Second-Order q-Difference Equations Involving Different Numbers of q

    Directory of Open Access Journals (Sweden)

    Thanin Sitthiwirattham

    2013-01-01

    Full Text Available We study a new class of three-point boundary value problems of nonlinear second-order q-difference equations. Our problems contain different numbers of q in derivatives and integrals. By using a variety of fixed point theorems (such as Banach’s contraction principle, Boyd and Wong fixed point theorem for nonlinear contractions, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative and Leray-Schauder degree theory, some new existence and uniqueness results are obtained. Illustrative examples are also presented.

  7. On the Robin-Transmission Boundary Value Problems for the Nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes Systems

    Science.gov (United States)

    Kohr, Mirela; de Cristoforis, Massimo Lanza; Wendland, Wolfgang L.

    2016-06-01

    The purpose of this paper is to study a boundary value problem of Robin-transmission type for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes systems in two adjacent bounded Lipschitz domains in {{{R}}n (nin {2,3})}, with linear transmission conditions on the internal Lipschitz interface and a linear Robin condition on the remaining part of the Lipschitz boundary. We also consider a Robin-transmission problem for the same nonlinear systems subject to nonlinear transmission conditions on the internal Lipschitz interface and a nonlinear Robin condition on the remaining part of the boundary. For each of these problems we exploit layer potential theoretic methods combined with fixed point theorems in order to show existence results in Sobolev spaces, when the given data are suitably small in {L^2}-based Sobolev spaces or in some Besov spaces. For the first mentioned problem, which corresponds to linear Robin and transmission conditions, we also show a uniqueness result. Note that the Brinkman-Forchheimer-extended Darcy equation is a nonlinear equation that describes saturated porous media fluid flows.

  8. Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2005-06-01

    Full Text Available In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations$ x^{(n}(t=f(t,x(t,x'(t,\\cdots,x^{(n-1}(t+e(t,\\;\\;0and the following multi-point boundary value conditions$ \\begin{array}{ll} x^{(i}(0=0\\;\\;for\\;i=0,1,\\cdots,n-3,\\\\ x^{(n-2}(0=\\alpha x^{(n-1}(\\xi,\\;\\;x^{(n-1}(1=\\beta x^{(n-2}(\\eta,\\end{array} \\eqno{(\\ast\\ast} $Sufficient conditions for the existence of at least one solution of the BVP$ (\\ast $ and $ (\\ast\\ast $ at resonance are established. This paper is directly motivated by Liu and Yu [India J. Pure Appl. Math., 33(4(2002475-494] and Qi [Acta Math. Appl. Sinica, 17(2(2001271-278].

  9. Holographic s-wave condensate with nonlinear electrodynamics: A nontrivial boundary value problem

    Science.gov (United States)

    Banerjee, Rabin; Gangopadhyay, Sunandan; Roychowdhury, Dibakar; Lala, Arindam

    2013-05-01

    In this paper, considering the probe limit, we analytically study the onset of holographic s-wave condensate in the planar Schwarzschild-AdS background. Inspired by various low-energy features of string theory, in the present work we replace the conventional Maxwell action with a (nonlinear) Born-Infeld action which essentially corresponds to the higher-derivative corrections of the gauge fields. Based on a variational method which is commonly known as the Sturm-Liouville eigenvalue problem and considering a nontrivial asymptotic solution for the scalar field, we compute the critical temperature for the s-wave condensation. The results thus obtained analytically agree well with the numerical findings [J. Jing and S. Chen, Phys. Lett. B 686, 68 (2010)]. As a next step, we extend our perturbative technique to compute the order parameter for the condensation. Interestingly, our analytic results are found to be of the same order as the numerical values obtained earlier.

  10. On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems

    CERN Document Server

    Hochman, Amit; White, Jacob K

    2011-01-01

    A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context of the 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss-Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nystr\\"{o}m method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented.

  11. Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations

    Directory of Open Access Journals (Sweden)

    2009-02-01

    Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.

  12. THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR THE SINGULARLY PERTURBED INITIAL BOUNDARY VALUE PROBLEMS OF THE REACTION DIFFUSION EQUATIONS IN A PART OF DOMAIN

    Institute of Scientific and Technical Information of China (English)

    刘其林; 莫嘉琪

    2001-01-01

    A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.

  13. On using enriched cover function in the Partition-of-unity method for singular boundary-value problems

    Science.gov (United States)

    Liu, X.; Lee, C. K.; Fan, S. C.

    Amongst the various approaches of `meshless' method, the Partition-of-unity concept married with the traditional finite-element method, namely PUFEM, has emerged to be competitive in solving the boundary-value problems. It inherits most of the advantages from both techniques except that the beauty of being `meshless' vanishes. This paper presents an alternative approach to solve singular boundary-value problems. It follows the basic PUFEM procedures. The salient feature is to enhance the quality of the influence functions, either over one single nodal cover or multi-nodal-covers. In the vicinity of the singularity, available asymptotic analytical solution is employed to enrich the influence function. The beauty of present approach is that it facilitates easy replacement of the influence functions. In other words, it favors the `influence-function refinement' procedure in a bid to search for more accurate solutions. It is analogous to the `p-version refinement' in the traditional finite-element procedures. The present approach can yield very accurate solution without adopting refined meshes. As a result, the quantities around the singularity can be evaluated directly once the nodal values are solved. No additional post-processing is needed. Firstly, the formulation of the present PUFEM approach is described. Subsequently, illustrative examples show the application to three classical singular benchmark problems having various orders of singularity. Results obtained through mesh refinements, single-nodal-cover refinements or multi-nodal-cover refinements are compared.

  14. Existence results for φ-Laplacian boundary value problems on time scales

    Directory of Open Access Journals (Sweden)

    Cabada Alberto

    2006-01-01

    Full Text Available This paper is devoted to proving the existence of the extremal solutions of a φ-Laplacian dynamic equation coupled with nonlinear boundary functional conditions that include as a particular case the Dirichlet and multipoint ones. We assume the existence of a pair of well-ordered lower and upper solutions.

  15. Quasilinearization for the periodic boundary value problem for systems of impulsive differential equations

    Directory of Open Access Journals (Sweden)

    2006-01-01

    Full Text Available The method of generalized quasilinearization for the system of nonlinear impulsive differential equations with periodic boundary conditions is studied. As a byproduct, the result for the system without impulses can be obtained, which is a new result as well.

  16. Trigonometric series adapted for the study of Dirichlet boundary-value problems of Lame systems

    Directory of Open Access Journals (Sweden)

    Boubakeur Merouani

    2015-07-01

    Full Text Available Several authors have used trigonometric series for describing the solutions to elliptic equations in a plane sector; for example, the study of the biharmonic operator with different boundary conditions, can be found in [2,9,10]. The main goal of this article is to adapt those techniques for the study of Lame systems in a sector.

  17. Trigonometric series adapted for the study of Dirichlet boundary-value problems of Lame systems

    OpenAIRE

    Boubakeur Merouani; Razika Boufenouche

    2015-01-01

    Several authors have used trigonometric series for describing the solutions to elliptic equations in a plane sector; for example, the study of the biharmonic operator with different boundary conditions, can be found in [2,9,10]. The main goal of this article is to adapt those techniques for the study of Lame systems in a sector.

  18. Nonlocal boundary value problem for strongly singular higher-order linear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    -, č. 33 (2013), s. 1-38 ISSN 1417-3875 Institutional support: RVO:67985840 Keywords : higher order linear differential equation * nonlocal boundary conditions * deviating argument Subject RIV: BA - General Mathematics Impact factor: 0.638, year: 2013 http://www.emis.de/journals/EJQTDE/p2108. pdf

  19. A Multi-Point, Boundary-Value Problem, Collocation Toolbox for the Continuation of sets of Constrained Orbit Segments

    DEFF Research Database (Denmark)

    Dankowicz, Harry; Schilder, Frank

    collocation algorithm allows for segment-dependent meshing and non-trivial boundary conditions involving internal mesh points and includes a full discretization of the corresponding variational equations. Several examples are chosen to illustrate the formalism and its implementation, including the......This paper presents a collocation toolbox for multi-point, boundary-value problems. This toolbox has been recently developed by the authors to support general-purpose parameter continuation of sets of constrained orbit segments, such as i) segmented trajectories in hybrid dynamical systems, for...... example, mechanical systems with impacts, friction, and switching control, ii) homoclinic orbits represented by an equilibrium point and a finite-time trajectory that starts and ends near this equilibrium point, and iii) collections of trajectories that represent quasi-periodic invariant tori. The...

  20. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

    Directory of Open Access Journals (Sweden)

    Suheel Abdullah Malik

    2014-01-01

    Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

  1. EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    Ye Yaojun

    2005-01-01

    The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div(|▽u|p-2▽u)= |u|mu, (x,t) ∈ [0,+∞) ×Ωwith p > 2 and m > 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded,the global nonexistence of solutions is verified by using the analysis method.

  2. Positive solutions to a generalized second-order three-point boundary-value problem on time scales

    Directory of Open Access Journals (Sweden)

    Hua Luo

    2005-02-01

    Full Text Available Let $mathbb{T}$ be a time scale with $0,T in mathbb{T}$. We investigate the existence and multiplicity of positive solutions to the nonlinear second-order three-point boundary-value problem $$displaylines{ u^{Delta abla}(t+a(tf(u(t=0,quad tin[0, T]subset mathbb{T},cr u(0=eta u(eta,quad u(T=alpha u(eta }$$ on time scales $mathbb{T}$, where 0, 0less than $alpha$ less than $frac{T}{eta}$, 0 less than $eta$ less than $frac{T-alphaeta}{T-eta}$ are given constants.

  3. FREE BOUNDARY VALUE PROBLEM FOR THE CYLINDRICALLY SYMMETRIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

    Institute of Scientific and Technical Information of China (English)

    Ruxu LIAN; Jian LIU

    2016-01-01

    In this paper, we investigate the free boundary value problem (FBVP) for the cylindrically symmetric isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, we prove that there exists a unique global strong solution which tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

  4. Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation

    OpenAIRE

    1997-01-01

    For the damped Boussinesq equation $u_{tt}-2bu_{txx}= -\\alpha u_{xxxx}+ u_{xx}+\\beta(u^2)_{xx},x\\in(0,\\pi),t > 0;\\alpha,b = const > 0,\\beta = const\\in R^1$ , the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the so...

  5. On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

    CERN Document Server

    Obukhov, Yuri N

    2007-01-01

    We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations $(D,H)$ (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths $(E,B)$ (which reflects flux conservation), and (c) the constitutive relation between $(D,H)$ and $(E,B)$. In the recent paper \\cite{Lakhtakia1}, Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.

  6. Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem

    OpenAIRE

    Lian, Wei-Cheng; Wang, Wei-Chuan; Cheng, Y. H.

    2011-01-01

    We study the nonlinear one-dimensional $p$-Laplacian equation $$ -(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of $f(s)/s^{(p-1)}$ when $s$ are at infinity and zero. These results are more general and complementary for previous known ones for the case $p=2$ and $q$ is nonnegative.

  7. Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Yanping Guo

    2007-01-01

    Full Text Available By using a new fixed-point theorem introduced by Avery and Peterson (2001, we obtain sufficient conditions for the existence of at least three positive solutions for the equation Δ2x(k−1+q(kf(k,x(k,Δx(k=0, for k∈{1,2,…,n−1}, subject to the following two boundary conditions: x(0=x(n=0 or x(0=Δx(n−1=0, where n≥3.

  8. The regularity of solutions for nonlinear degenerate elliptic boundary value problems

    International Nuclear Information System (INIS)

    In the present paper, with the aid of the techniques of micro-local analysis, a regularity theorem of the solutions to Dirichlet problem for a class of nonlinear degenerate elliptic equations is given. (author). 8 refs

  9. Manifold and metric in numerical solution of the quasi-static electromagnetic boundary value problems

    OpenAIRE

    Raumonen, Pasi; Suuriniemi, Saku; Tarhasaari, Timo; Kettunen, Lauri

    2007-01-01

    Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds over the traditional approach in practical problems of modelling. With a structural approach, it outlines the role and interdependence of coordinate systems, metric, constitutive equations, and fields, and relates them to practical problems of quasi-static co...

  10. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Mesloub Said

    2008-01-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  11. Solvability of fractional multi-point boundary-value problems with p-Laplacian operator at resonance

    Directory of Open Access Journals (Sweden)

    Tengfei Shen

    2014-02-01

    Full Text Available In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with $p$-Laplacian operator: $$\\displaylines{ D_{0^+}^\\beta \\varphi_p (D_{0^+}^\\alpha u(t = f(t,u(t,D_{0^+}^{\\alpha - 2} u(t,D_{0^+}^{\\alpha - 1} u(t, D_{0^+}^\\alpha u(t,\\quad t \\in (0,1, \\cr u(0 = u'(0=D_{0^+}^\\alpha u(0 = 0,\\quad D_{0^+}^{\\alpha - 1} u(1 = \\sum_{i = 1}^m {\\sigma_i D_{0^+}^{\\alpha - 1} u(\\eta_i } , }$$ where $2 < \\alpha \\le 3$, $0 < \\beta \\le 1$, $3 < \\alpha + \\beta \\le 4$, $\\sum_{i = 1}^m {\\sigma_i } = 1$, $D_{0^+}^\\alpha$ is the standard Riemann-Liouville fractional derivative. $\\varphi_{p}(s=|s|^{p-2}s$ is p-Laplacians operator. The existence of solutions for above fractional boundary value problem is obtained by using the extension of Mawhin's continuation theorem due to Ge, which enrich konwn results. An example is given to illustrate the main result.

  12. Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations

    Directory of Open Access Journals (Sweden)

    George N. Galanis

    2005-10-01

    Full Text Available In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem$$ -[phi _{p}(u']'=q(tf(t,u(t,quad 0boundary-value problem remains away from the origin for the case where the nonlinearity is sublinear and so we avoid its singularity at $u=0$.

  13. Initial-boundary-value problems for discrete evolution equations: discrete linear Schrödinger and integrable discrete nonlinear Schrödinger equations

    International Nuclear Information System (INIS)

    We present a method to solve initial-boundary-value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A S Fokas to solve initial-boundary-value problems for linear and integrable nonlinear partial differential equations via an extension of the inverse scattering transform. The method takes advantage of the Lax pair formulation for both linear and nonlinear equations, and is based on the simultaneous spectral analysis of both parts of the Lax pair. A key role is also played by the global algebraic relation that couples all known and unknown boundary values. Even though additional technical complications arise in discrete problems compared to continuum ones, we show that a similar approach can also solve initial-boundary-value problems for linear and integrable nonlinear differential-difference equations. We demonstrate the method by solving initial-boundary-value problems for the discrete analogue of both the linear and the nonlinear Schrödinger equations, comparing the solution to those of the corresponding continuum problems. In the linear case we also explicitly discuss Robin-type boundary conditions not solvable by Fourier series. In the nonlinear case, we also identify the linearizable boundary conditions, we discuss the elimination of the unknown boundary datum, we obtain explicitly the linear and continuum limit of the solution, and we write the soliton solutions

  14. Solvability of initial boundary value problem for the equations of filtration in poroelastic media

    Science.gov (United States)

    Tokareva, M. A.

    2016-06-01

    The study is devoted to the mathematical model of fluid filtration in poroelastic media. The laws of conservation of mass for each phase, Darcy's law for fluid phase, the rheological law and the general equation of conservation of momentum for system describe this process. The local solvability of the problem is proved in this paper for the case in which the density of the mass forces is equal to zero and the fluid is compressible.

  15. The method of lower and upper solutions for n th-order periodic boundary value problems

    Directory of Open Access Journals (Sweden)

    Alberto Cabada

    1994-01-01

    Full Text Available In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(n(t=f(t,u(t;u(i(a−u(i(b=λi∈ℝ,i=0,…,n−1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n≥3 with either α≤β or α≥β.

  16. Sign-Changing and Extremal Constant-Sign Solutions of Nonlinear Elliptic Neumann Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Winkert Patrick

    2010-01-01

    Full Text Available Our aim is the study of a class of nonlinear elliptic problems under Neumann conditions involving the -Laplacian. We prove the existence of at least three nontrivial solutions, which means that we get two extremal constant-sign solutions and one sign-changing solution by using truncation techniques and comparison principles for nonlinear elliptic differential inequalities. We also apply the properties of the Fu ik spectrum of the -Laplacian and, in particular, we make use of variational and topological tools, for example, critical point theory, Mountain-Pass Theorem, and the Second Deformation Lemma.

  17. Convergence of a continuous BGK model for initial boundary-value problems for conservation laws

    Directory of Open Access Journals (Sweden)

    Driss Seghir

    2001-11-01

    Full Text Available We consider a scalar conservation law in the quarter plane. This equation is approximated in a continuous kinetic Bhatnagar-Gross-Krook (BGK model. The convergence of the model towards the unique entropy solution is established in the space of functions of bounded variation, using kinetic entropy inequalities, without special restriction on the flux nor on the equilibrium problem's data. As an application, we establish the hydrodynamic limit for a $2imes2$ relaxation system with general data. Also we construct a new family of convergent continuous BGK models with simple maxwellians different from the $chi$ models.

  18. Boundary value problems for the 2nd-order Seiberg-Witten equations

    Directory of Open Access Journals (Sweden)

    Celso Melchiades Doria

    2005-02-01

    Full Text Available It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition ℋ is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict the problem to the Coulomb subspace 𝒞αℭ of configuration space. The coercivity of the 𝒮𝒲α-functional, when restricted into the Coulomb subspace, imply the existence of a weak solution. The regularity then follows from the boundedness of L∞-norms of spinor solutions and the gauge fixing lemma.

  19. Multiple Positive Solutions to Third-Order Three-Point Singular Semipositone Boundary Value Problem

    Indian Academy of Sciences (India)

    Huimin Yu; L Haiyan; Yansheng Liu

    2004-11-01

    By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: \\begin{equation*}\\begin{cases}x'"(t)- f(t,x)=0, & t\\in(0, 1);\\\\ x(0)=x'()=x"(1)=0,\\end{cases}\\end{equation*} where $\\frac{1}{2} < < 1$, the non-linear term $f(t,x): (0,1)×(0,=∞)→(-∞ +∞)$ is continuous and may be singular at = 0, = 1, and = 0, also may be negative for some values of and , is a positive parameter.

  20. Periodic boundary-value problems and the Dancer-Fucik spectrum under conditions of resonance

    Directory of Open Access Journals (Sweden)

    David A. Bliss

    2011-08-01

    Full Text Available We prove the existence of solutions to the nonlinear $2 pi$-periodic problem $$displaylines{ u''(x+mu u^+(x-u u^-(x+g(x,u(x=f(x,,quad xin (0,2pi,,cr u(0-u(2pi =0 ,, quad u'(0 - u'(2pi=0, }$$ where the point $(mu,u$ lies in the Dancer-Fucik spectrum, with $$ 0< frac{4}{9}mu leqslant u

  1. Periodic boundary-value problems and the Dancer-Fucik spectrum under conditions of resonance

    OpenAIRE

    David A. Bliss; James Buerger; Adolfo J. Rumbos

    2011-01-01

    We prove the existence of solutions to the nonlinear $2 pi$-periodic problem $$displaylines{ u''(x)+mu u^+(x)-u u^-(x)+g(x,u(x))=f(x),,quad xin (0,2pi),,cr u(0)-u(2pi) =0 ,, quad u'(0) - u'(2pi)=0, }$$ where the point $(mu,u)$ lies in the Dancer-Fucik spectrum, with $$ 0< frac{4}{9}mu leqslant u

  2. 具有转向点的奇摄动边值问题%THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS WITH TURNING POINT

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2000-01-01

    讨论了具有转向点的奇摄动椭圆方程边值问题并利用多重尺度法和比较定理,研究了边值问题解的渐近性态.%The singularly perturbed elliptic equation boundary value problem with turning point is considered. Using the method of multiple scales and the comparison theorem, the asymptotic behavior of solution for the boundary value problem is studied.

  3. DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH CHANGING SIGN NONLINEARITIES

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities.

  4. 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.

  5. Existence of a positive solution for an nth order boundary value problem for nonlinear difference equations

    OpenAIRE

    Susan D. Lauer; Johnny Henderson

    1997-01-01

    The nth order eigenvalue problem:                                          Δnx(t)=(−1)n−kλf(t,x(t)),          t∈[0,T],x(0)=x(1)=⋯=x(k−1)=x(T+k+1)=⋯=x(T+n)=0, is considered, where n≥2 and k∈{1,2,â...

  6. The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Nonlinear Higher Order Two-Point Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Navnit Jha

    2014-01-01

    Full Text Available An efficient algorithm for the numerical solution of higher (even orders two-point nonlinear boundary value problems has been developed. The method is third order accurate and applicable to both singular and nonsingular cases. We have used cubic spline polynomial basis and geometric mesh finite difference technique for the generation of this new scheme. The irreducibility and monotone property of the iteration matrix have been established and the convergence analysis of the proposed method has been discussed. Some numerical experiments have been carried out to demonstrate the computational efficiency in terms of convergence order, maximum absolute errors, and root mean square errors. The numerical results justify the reliability and efficiency of the method in terms of both order and accuracy.

  7. Boundary-value problem for a counterrotating electrical discharge in an axial magnetic field. [plasma centrifuge for isotope separation

    Science.gov (United States)

    Hong, S. H.; Wilhelm, H. E.

    1978-01-01

    An electrical discharge between two ring electrodes embedded in the mantle of a cylindrical chamber is considered, in which the plasma in the anode and cathode regions rotates in opposite directions under the influence of an external axial magnetic field. The associated boundary-value problem for the coupled partial differential equations describing the azimuthal velocity and radial current-density fields is solved in closed form. The velocity, current density, induced magnetic induction, and electric fields are presented for typical Hartmann numbers, magnetic Reynolds numbers, and geometry parameters. The discharge is shown to produce anodic and cathodic plasma sections rotating at speeds of the order 1,000,000 cm/sec for conventional magnetic field intensities. Possible application of the magnetoactive discharge as a plasma centrifuge for isotope separation is discussed.

  8. Existence of positive solutions for boundary-value problems for singular higher-order functional differential equations

    Directory of Open Access Journals (Sweden)

    Chuanzhi Bai

    2006-07-01

    Full Text Available We study the existence of positive solutions for the boundary-value problem of the singular higher-order functional differential equation $$displaylines{ (L y^{(n-2}(t+h(tf(t, y_t=0, quad hbox{for } tin [0, 1],cr y^{(i}(0 = 0, quad 0 leq i leq n - 3, cr alpha y^{(n-2}(t-eta y^{(n-1} (t=eta (t, quad hbox{for } t in [- au, 0],cr gamma y^{(n-2}(t + delta y^{(n-1}(t = xi (t, quad hbox{for } t in [1, 1 + a], }$$ where $ Ly := -(p y'' + q y$, $p in C([0, 1],(0, + infty$, and $q in C([0, 1], [0, + infty$. Our main tool is the fixed point theorem on a cone.

  9. Global uniqueness in inverse boundary value problems for the Navier–Stokes equations and Lamé system in two dimensions

    International Nuclear Information System (INIS)

    We consider inverse boundary value problems for the Navier–Stokes equations and the isotropic Lamé system in two dimensions. The question of global uniqueness for these inverse problems, without any smallness assumptions on unknown coefficients, has been a longstanding open problem for the Navier–Stokes equations and the isotropic Lamé system in two dimensions. We prove the global uniqueness for both inverse boundary value problems. Our methodology is the same for both systems. The key is the construction of complex geometric optics solutions after decoupling the systems into weakly coupling systems. (papers)

  10. Unique solvability of some two-point boundary value problems for linear functional differential equations with singularities

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Samoilenko, A. M.

    2007-01-01

    Roč. 41, - (2007), s. 115-136. ISSN 1512-0015 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-point problem * functional differential equation * singular boundary problem Subject RIV: BA - General Mathematics

  11. A third order of accuracy difference scheme for Dirichlet type overdermined problem with mixed boundary value conditions

    Science.gov (United States)

    Ashyralyyev, Charyyar; Dedeturk, Mutlu

    2016-08-01

    Approximation of Dirichlet type overdetermined multidimensional elliptic problem with Dirichlet-Neumann boundary conditions are discussed. A third order of accuracy difference scheme for its approximate solution is proposed. The stability, almost coercive stability and coercive stability inequalities for the solution of constructed difference scheme are established. Test example for a two-dimensional elliptic problem is presented.

  12. Nonlinear Boundary Value Problem for Concave Capillary Surfaces Occurring in Single Crystal Rod Growth from the Melt

    Directory of Open Access Journals (Sweden)

    Agneta Maria Balint

    2008-12-01

    Full Text Available The boundary value problem z″=((ρ⋅g⋅z−p/γ[1+(z′2]3/2−(1/r⋅[1+(z′2]⋅z′, r∈[r1, r0], z′(r1=−tan⁡(π/2−αg, z′(r0=−tan⁡αc, z(r0=0, and z(r is strictly decreasing on [r1,r0], is considered. Here, 0boundary value problem (NLBVP. Numerical illustration is given. This kind of results is useful in the experiment planning and technology design of single crystal rod growth from the melt by edge-defined film-fed growth (EFG method. With this aim, this study was undertaken.

  13. Existence and smoothness of solutions to second initial boundary value problems for Schrodinger systems in cylinders with non-smooth bases

    Directory of Open Access Journals (Sweden)

    Nguyen Manh Hung

    2008-03-01

    Full Text Available In this paper, we consider the second initial boundary value problem for strongly general Schrodinger systems in both the finite and the infinite cylinders $Q_T, 0problem are given.

  14. Oscillation Analysis for Vector Neutral Parabolic Robin Boundary Value Problem%向量中立型抛物Robin边值问题的振动性分析

    Institute of Scientific and Technical Information of China (English)

    罗李平

    2014-01-01

    The oscillation for a class of vector neutral parabolic boundary value problems is investigated .By employing inner product reducing dimension method and calculus technique ,some new sufficient conditions for the H-oscillation of all solutions of the boundary value problems are established under Robin boundary value condition ,where H is a unit vector .%研究了一类向量中立型抛物边值问题的振动性,借助内积降维方法和微积分技巧,建立了该类边值问题在Ro bin边值条件下所有解 H-振动的若干新的充分条件,其中H是一个单位向量。

  15. The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

    Science.gov (United States)

    Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun

    1993-01-01

    The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

  16. Impulsive periodic boundary value problem and topological degree. Dedicated to Lina Fazulovna Rakhmatullina and Nikolai Viktorovich Azbelev on the occasion of their jubilees

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    2002-01-01

    Roč. 9, 3-4 (2002), s. 471-498. ISSN 0793-1786 R&D Projects: GA ČR GA201/01/1451; GA ČR GA201/01/1199 Keywords : boundary value problem%ordinary differential equation Subject RIV: BA - General Mathematics

  17. Global superconvergence and a posteriori error estimators of the finite element method for a quasi-linear elliptic boundary value problem of nonmonotone type

    Czech Academy of Sciences Publication Activity Database

    Liu, L.; Liu, T.; Křížek, Michal; Lin, T.; Zhang, S.

    2004-01-01

    Roč. 42, č. 4 (2004), s. 1729-1744. ISSN 0036-1429 R&D Projects: GA AV ČR(CZ) IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : nonlinear boundary value problem * finite element s * supercloseness Subject RIV: BA - General Mathematics Impact factor: 1.106, year: 2004

  18. Positive solutions of some three-point boundary value problems via fixed point index for weakly inward A-proper maps

    OpenAIRE

    Gennaro Infante

    2005-01-01

    We use the theory of fixed point index for weakly inward A-proper maps to establish the existence of positive solutions of some second-order three-point boundary value problems in which the highest-order derivative occurs nonlinearly.

  19. Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2009-01-01

    Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

  20. A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method

    Directory of Open Access Journals (Sweden)

    Chein-Shan Liu

    2013-01-01

    Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.

  1. Solvability of boundary value problems with Riemann-Stieltjes Δ-integral conditions for second-order dynamic equations on time scales at resonance

    OpenAIRE

    Li Yongkun; Shu Jiangye

    2011-01-01

    Abstract In this paper, by making use of the coincidence degree theory of Mawhin, the existence of the nontrivial solution for the boundary value problem with Riemann-Stieltjes Δ-integral conditions on time scales at resonance x Δ Δ ( t ) = f ( t , x ( t ) , x Δ ( t ) ) + e ( t ) , a . e . t ∈ [ 0 , T ] T , x Δ ( 0 ) = 0 , x ( T ) = ∫ 0 T x σ ( s ) Δ g ...

  2. Numerical Algorithm Based on Quintic Nonpolynomial Spline for Solving Third-Order Boundary Value Problems Associated with Draining and Coating Flows

    Institute of Scientific and Technical Information of China (English)

    Pankaj Kumar SRIVASTAVA; Manoj KUMAR

    2012-01-01

    A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows.The authors show that the approximate solutions obtained by the numerical algorithm developed by using nonpolynomial quintic spline functions are better than those produced by other spline and domain decomposition methods.The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach.

  3. Positive solutions of a three-point boundary-value problem for differential equations with damping and actively bounded delayed forcing term

    Directory of Open Access Journals (Sweden)

    George L. Karakostas

    2006-08-01

    Full Text Available We provide sufficient conditions for the existence of positive solutions of a three-point boundary value problem concerning a second order delay differential equation with damping and forcing term whose the delayed part is an actively bounded function, a meaning introduced in [19]. By writing the damping term as a difference of two factors one can extract more information on the solutions. (For instance, in an application, given in the last section, we can give the exact value of the norm of the solution.

  4. On constructive investigation of a class of non-linear boundary value problems for functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.

    2013-01-01

    Roč. 29, č. 1 (2013), s. 91-108. ISSN 1584-2851 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-point boundary condition * functional differential equation * successive approximations Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2013 http://carpathian.ubm.ro/issues/OA_cjm_29_2013_091-108. pdf

  5. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  6. The Similar Structure Method Solving the Boundary Value Problem of Bessel Equations%求解Bessel方程的边值问题的相似结构法

    Institute of Scientific and Technical Information of China (English)

    陈宗荣; 李顺初

    2011-01-01

    In this paper, we solve the general boundary value problem of Bessel equations, and obtain the similar structure and the similar kernel function of solutions. A new idea and method for solving this kind of problems is formed: so called "similar structure construction". This idea and method can be used to analyze inner properties of solutions, to solve some practical problems and to write analytical softwares.%对Bessel方程的一般边值问题进行求解,得到了解式的相似结构和相似核函数及求解Bessel方程边值问题的一个新思想和新方法:相似结构构造法.该方法有利于进一步分析解的内在规律、解决相应的应用问题、方便编制相应的分析软件.

  7. COMBINATIVE PRECONDITIONERS OF MODIFIED INCOMPLETE CHOLESKY FACTORIZATION AND SHERMAN-MORRISON-WOODBURY UPDATE FOR SELF-ADJOINT ELLIPTIC DIRICHLET-PERIODIC BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Zhong-zhi Bai; Gui-qing Li; Lin-zhang Lu

    2004-01-01

    For the system of linear equations arising from discretization of the second-order selfadjoint elliptic Dirichlet-periodic boundary value problems, by making use of the special structure of the coefficient matrix we present a class of combinative preconditioners which are technical combinations of modified incomplete Cholesky factorizations and ShermanMorrison-Woodbury update. Theoretical analyses show that the condition numbers of the preconditioned matrices can be reduced to (h-1), one order smaller than the condition number (h-2) of the original matrix. Numerical implementations show that the resulting preconditioned conjugate gradient methods are feasible, robust and efficient for solving this class of linear systems.

  8. Finding Solutions to the Picard Boundary Value Problem via Homotopy Method%用同伦方法求Picard边值问题的解

    Institute of Scientific and Technical Information of China (English)

    李兰; 徐旭

    2008-01-01

    This paper deals with the problem of finding solutions to the Picard boundary problem. In our approach, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of" the equa tion we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem.

  9. Positive and Dead-Core Solutions of Two-Point Singular Boundary Value Problems with ϕ-Laplacian

    OpenAIRE

    Staněk Svatoslav

    2010-01-01

    The paper discusses the existence of positive solutions, dead-core solutions, and pseudo-dead-core solutions of the singular problem , , . Here is a positive parameter, , , , , is singular at and may be singular at .

  10. Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities

    OpenAIRE

    An Yulian

    2011-01-01

    We consider the nonlinear eigenvalue problems , , , , where , and for with and satisfies for , and , where . We investigate the global structure of nodal solutions by using the Rabinowitz's global bifurcation theorem.

  11. 非线性离散周期边值问题的可解性%Solvability for nonliner discrete periodic boundary value problems

    Institute of Scientific and Technical Information of China (English)

    董士杰

    2012-01-01

    在非线性项f(u)在原点满足渐近线性增长、无穷远处满足超线性或次线性增长条件下,研究了二阶非线性离散周期边值问题的可解性解.应用Robinowitz全局分歧定理,给出了边值问题正解全局行为的完整描述,并确定了参数的最佳区间.%Under the condition that nonlinearity f(u) satisfies asymptotically linear growth at the origin and sublinear growth or suplinear growth at the infinity, the solvability for nonliner discrete periodic boundary value problems are discussed. By using Robinowitz global bifurcation theorem, a complete description of the global behavior of positive solution for the boundary value problem is given, and the optimal interval of a positive parameter is determined.

  12. Positive Solutions for System of 2-th Order Sturm-Liouville Boundary Value Problems on time Scales

    Indian Academy of Sciences (India)

    K R Prasad; A Kameswara Rao; B Bharathi

    2014-02-01

    Intervals of the parameters and are determined for which there exist positive solutions to the system of dynamic equations \\begin{align*}(-1)^n u^{^{2n}}(t)+ p(t) f(((t)))=0, & t\\in[a, b],\\\\ (-1)^n^{^{2n}} (t) + q(t)g (u((t))) = 0, & t\\in [a, b],\\end{align*} satisfying the Sturm–Liouville boundary conditions \\begin{align*}& _{i+1}u^{^{2i}}(a)-_{i+1}u^{^{2i+1}}(a)=0, _{i+1}u^{^{2i}}((b))+_{i+1}u^{^{2i+1}}((b))=0,\\\\ & _{i+1}^{^{2i}}(a)-_{i+1}^{^{2i+1}}(a)=0,_{i+1}^{^{2i}}((b))+_{i+1}^{^{2i+1}}((b))=0,\\end{align*} for $0≤ i≤ n-1$. To this end we apply a Guo–Krasnosel’skii fixed point theorem.

  13. EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function,μ is the scaled Rayleigh number,K=1 and α represents the effects of a heat transfer finite Biot number.The cofficients β,δ and γ do not vanish when the boundary conditions at top and bottom are not identical (β≠0,δ≠0) or non Boussinesq effects are taken into account (γ ≠ 0).In this paper,the Knobloch equation with α > 0 is considered,the globai existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively.

  14. A Class of Bridges of Iterated Integrals of Brownian Motion Related to Various Boundary Value Problems Involving the One-Dimensional Polyharmonic Operator

    Directory of Open Access Journals (Sweden)

    Aimé Lachal

    2011-01-01

    Full Text Available Let ((∈[0,1] be the linear Brownian motion and ((∈[0,1] the (−1-fold integral of Brownian motion, with being a positive integer: ∫(=0((−−1/(−1!d( for any ∈[0,1]. In this paper we construct several bridges between times 0 and 1 of the process ((∈[0,1] involving conditions on the successive derivatives of at times 0 and 1. For this family of bridges, we make a correspondence with certain boundary value problems related to the one-dimensional polyharmonic operator. We also study the classical problem of prediction. Our results involve various Hermite interpolation polynomials.

  15. Construction of Lower and Upper Functions and Their Application to Regular and Singular Periodic Boundary Value Problems

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    2001-01-01

    Roč. 47, - (2001), s. 3937-3948. ISSN 0362-546X R&D Projects: GA ČR GA201/98/0318; GA ČR GA201/01/1199 Keywords : second order nonlinear ordinary differential equation %periodic solution%singular problem Subject RIV: BA - General Mathematics Impact factor: 0.406, year: 2001

  16. On a two-point boundary value problem for the second order linear functional differential equations with monotone operators

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Šremr, Jiří

    2006-01-01

    Roč. 13, 3-4 (2006), s. 519-537. ISSN 0793-1786 R&D Projects: GA ČR(CZ) GP201/04/P183 Institutional research plan: CEZ:AV0Z10190503 Keywords : functional differential equation * monotone operator * Dirichlet problem Subject RIV: BA - General Mathematics

  17. Material equations for rock salt under mechanical and thermal load including treatment of boundary value problems by the finite element method

    Energy Technology Data Exchange (ETDEWEB)

    Olschewski, J.; Stein, E.; Wagner, W.; Wetjen, D.

    1981-01-01

    This paper is a first step in the development of thermodynamically consistent material equations for inelastic materials, such as polycrystalline rock salt. In this context it is of particular importance to reduce the number and the structure of the internal variables, in order to allow for a fit with available experimental data. As an example this is demonstrated in detail in the case of the so-called dislocation model. As physical non-linearities and in addition also geometrical non-linearities lead to an inhomogeneous deformation - and stress state even in the case of simple samples, boundary value problems have to be studied, in order to test the material equations. For this purpose the finite element method has been used.

  18. Numerical method of solution of a boundary value problem for the coupled integro-differential equations (The Bethe-Salpeter equation)

    International Nuclear Information System (INIS)

    We proposed the algorithm for umerical solving a boundary value problem for two-quark bound states described by the Salpeter equation with potential V0r2-αs/r which is coupled integro-differential equations depending on physical parameters m0 and αs. In this algorithm an iteration scheme of the continuous analogy of Newton's method, with corresponding choice of the iteration parameter, is realized. It is shown that using the continuation over parameter (m0, αs) method allows one to extend considerably a region of convergence of the iteration method. The solutions of the Salpeter equation for set of parameters m0 and αs are obtained, which reproduce the results are available (when m0=αs=0). 17 refs.; 1 fig.; 2 tabs

  19. Existence and Uniqueness of Positive Solutions of Boundary-Value Problems for Fractional Differential Equations with p-Laplacian Operator and Identities on the Some Special Polynomials

    Directory of Open Access Journals (Sweden)

    Erdoğan Şen

    2013-01-01

    Full Text Available We consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator D0+β(ϕp(D0+αu(t+a(tf(u=0, 01, ϕp-1=ϕq, 1/p+1/q=1,0⩽γ0 are parameters, a:(0,1→[0,+∞, and f:[0,+∞→[0,+∞ are continuous. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence results for positive solutions, in terms of the parameters λ and μ are obtained. The uniqueness of positive solution on the parameters λ and μ is also studied. In the final section of this paper, we derive not only new but also interesting identities related special polynomials by which Caputo fractional derivative.

  20. K-复调和函数的Schwarz边值问题%Schwarz's boundary value problem for K- complex harmonic function

    Institute of Scientific and Technical Information of China (English)

    张建元; 刘俊; 张毅敏; 张昕

    2012-01-01

    In the paper,the Schwarz's type mixed K- integral is defined and studied within elliptic domain B(0, R) (k): | z(k) | ≤R to obtain the solutions of Schwarz's boundary value problem within K-complex harmonic function. The conclusion is the continuation and application of the solution K- complex harmonic function with the corresponding theories of the analytic function and harmonic function.%在椭圆域B(0,R)(k)={z:|z(k)|≤R}上定义和讨论了Schwarz混合型K-积分,并用它来求K-复调和函数类H(D(k))中的Schwarz边值问题的解.所得结论包含了前人的有关结果.

  1. 不连续二阶周期边值问题的可解性%Solvability of Discontinuous Second- Order Periodic Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    姚庆六

    2006-01-01

    The existence of solution is studied for a class of second - order periodic boundary value problems with first applying Leray - Schauder fixed point theorem, two exislence theorems are established. First theorem shows that the class of problems has at least one solution provided the integral of height function is appropriate. Second theorem shows that the existence of solution is possible under suitable conditions when the limit of growth of nonlinear term at infinity is an unbounded function.%考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性,其中非线性项是Carathèodory函数.通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理.第一个定理表明只要高度函数的积分是适当的,这类问题至少有一个解.第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解.

  2. Boundary and eigenvalue problems in mathematical physics

    CERN Document Server

    Sagan, Hans

    1989-01-01

    This well-known text uses a limited number of basic concepts and techniques - Hamilton's principle, the theory of the first variation and Bernoulli's separation method - to develop complete solutions to linear boundary value problems associated with second order partial differential equations such as the problems of the vibrating string, the vibrating membrane, and heat conduction. It is directed to advanced undergraduate and beginning graduate students in mathematics, applied mathematics, physics, and engineering who have completed a course in advanced calculus. In the first three chapters,

  3. A realization theory for autonomous boundary-value linear systems

    OpenAIRE

    Nikoukhah, Ramine

    1989-01-01

    A frequency-domain realization theory is developed for the class of autonomous- , but not necessarily stationary, boundary-value linear systems. It is shown that this realization problem, which consists of constructing autonomous boundary-value linear systems from prescribed weighting patterns, reduces to the factorization of several rational matrices in two variables having separable denominators. This factorization problem is examined and a method is given for constructing minimal factoriza...

  4. 最小二乘法求解三类卫星重力梯度边值问题%Solving Three Types of Satellite Gravity Gradient Boundary Value Problems by Least-Squares

    Institute of Scientific and Technical Information of China (English)

    徐新禹; 李建成; 邹贤才; 褚永海

    2007-01-01

    The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γzz},{Γxz,Γyz} and {Γzz -Γyy,2Γxy} are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field.

  5. 求解一类 Riccati - Bessel 方程边值问题的新方法%A New Method of Solving the Boundary Value Problem of a Class of Riccati - Bessel Equation

    Institute of Scientific and Technical Information of China (English)

    王强; 李顺初; 蒲俊

    2015-01-01

    This paper solved a boundary value problem of Riccati - Bessel equation;and the similar kernel function and similar structure of the solution were obtained. By further analysis and solving this class of boundary value problem,the guiding functions were firstly constructed by using two linearly independent solutions of Riccati- Bessel equation,and then the similar kernel function was assembled by the guiding functions and coefficient of right boundary value condition. The solution to the boundary value problem was assembled by similar kernel func-tion and coefficient of left boundary value condition. Therefore a new idea is put forward for solving this class of boundary value problem of Riccati - Bessel equation:similar structure.%针对 Riccati - Bessel 方程一类边值问题进行求解,获得了解式的相似核函数和相似结构,通过进一步分析,发现求解该类边值问题可先利用 Riccati - Bessel 方程的两个线性无关解构造引解函数,再结合右边值条件的系数组装得到相似核函数;通过相似核函数和左边值条件的系数组装就可以得到 Riccati - Bessel 方程边值问题的解,由此提出了解决该类 Riccati - Bessel 方程边值问题的一种新思路———相似构造。

  6. Problems of matter-antimatter boundary layers

    International Nuclear Information System (INIS)

    This paper outlines the problems of the quasi-steady matter-antimatter boundary layers discussed in Klein-Alfven's cosmological theory, and a crude model of the corresponding ambiplasma balance is presented: (i) at interstellar particle densities, no well-defined boundary layer can exist in presence of neutral gas, nor can such a layer be sustained in an unmagnetized fully ionized ambiplasma. (ii) Within the limits of applicability of the present model, sharply defined boundary layers are under certain conditions found to exist in a magnetized ambiplasma. Thus, at beta values less than unity, a steep pressure drop of the low-energy components of matter and antimatter can be balanced by a magnetic field and the electric currents in the ambiplasma. (iii) The boundary layer thickness is of the order of 2x0 approximately 10/BT0sup(1/4) meters, where B is the magnetic field strength in MKS units and T0 the characteristic temperature of the low-energy components in the layer. (Auth.)

  7. Foliation of the space of periodic boundary-value problems by hypersurfaces corresponding to fixed lengths of the n th spectral lacuna

    Science.gov (United States)

    Dymarskii, Ya M.; Evtushenko, Yu A.

    2016-05-01

    The space of one-dimensional stationary Schrödinger equations with a real-valued periodic potential and periodic boundary conditions is considered. An analytic and topological description of its foliation by hypersurfaces defined by the condition that the nth spectral lacuna has fixed length is given. The case when a lacuna degenerates into a point gives the Schwarzian derivative and the Arnold manifold. In the nondegenerate case, the linking number of the loop formed by potentials with shifted argument and an Arnold manifold is calculated. Bibliography: 12 titles.

  8. 一类分数阶微分方程反周期边值问题解的存在性%Existence Results for Anti-periodic Boundary Value Problems Involving Fractional Differential Equations

    Institute of Scientific and Technical Information of China (English)

    朱晓慧

    2011-01-01

    This paper explores the existence results for anti-periodic boundary value problems involving nonlinear fractional differential equations.With the integral equations and based on Banach's space fixed point theorem and Schaeffor's theorem,the uniqueness of existence and sufficient conditions for at least one solution for anti-periodic boundary value problems are obtained.%讨论一类非线性分数阶反周期边值问题解存在性情况,通过构造反周期问题等价积分方程,利用B anach空间不动点定理和Schaeffor定理分别给出了反周期边值问题解存在唯一性和至少存在一解的充分条件。

  9. Existence and uniqueness of solutions for anti-periodic fractional boundary value problems%分数阶微分方程反周期边值问题解的存在性与唯一性

    Institute of Scientific and Technical Information of China (English)

    张宁; 史小艺; 薛婷婷

    2012-01-01

    研究了一类分数阶微分方程反周期边值问题,在连续函数f:[0,T]×R→R满足一定条件下,利用不动点定理得到了分数阶微分方程反周期边值问题解的存在性与唯一性,并举例说明了结论的适用性.%This paper discusses a class of anti-periodic fractional boundary value problems.As the continuous function f:×R→R can meet certain conditions,the existence and uniqueness of solutions for anti-periodic fractional boundary value problems are obtained by applying the fixed point theorem.In the end,several examples are given to illustrate the results.

  10. Continuity of the free boundary in elliptic problems with Neuman boundary condition

    Directory of Open Access Journals (Sweden)

    Abderachid Saadi

    2015-06-01

    Full Text Available We show the continuity of the free boundary in a class of two dimensional free boundary problems with Neuman boundary condition, which includes the aluminium electrolysis problem and the heterogeneous dam problem with leaky boundary condition.

  11. EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L2-SPACES%一族非线性边值问题在L2(Ω)空间中解的存在性

    Institute of Scientific and Technical Information of China (English)

    魏利; 周海云

    2005-01-01

    By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta(1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2(Ω) are studied.The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhens previous papers.Especially,some new techniques are used in this paper.

  12. Existence of solution for anti-periodic boundary value problem of fractional differential equation%分数阶微分方程反周期边值问题解的存在性

    Institute of Scientific and Technical Information of China (English)

    周宗福; 贾宝瑞

    2011-01-01

    The boundary value problem of fractional differential equations had attracted many authors to study this subject, due to its valuable theory and widely applied background. Anti-periodic boundary value problem was an important class of it. In this paper, by employing of Krasnoselskii fixed point theorem and some analysis techniques, we studied the anti-periodic boundary value problem for a kind of fractional integraldifferential equation. A sufficient condition for the existence of anti-periodic boundary value problem's solution was obtained. Compared with the previous results, the result in this paper was easier to be verified and extended some known results to some extent.%分数阶微分方程边值问题具有良好的理论价值和广泛的应用背景,一直吸引不少学者对其进行研究.反周期边值问题是边值问题中重要的一类.作者利用Krasnoselskii不动点定理和一些分析技巧,研究一类分数阶微分积分方程反周期边值问题,获得了反周期边值问题解存在的一个充分条件.与以往的结果相比较,论文中所得的条件容易验证,在一定程度上推广了已有的结论.

  13. 具有p-Laplacian算子的二阶微分方程Picard边值问题%Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations

    Institute of Scientific and Technical Information of China (English)

    刘玉记

    2011-01-01

    Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations {[φ(x'(t))]' + kx(t) + g(t, x(t)) = p(t), t ∈ (0, π)x(0) = x(π) = 0are established, where [φ(x')]' = (|x'|p-2x')' with p > 1. Our result is new even when [φ(x')]' = x" in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.

  14. 一阶差分方程周期边值问题一个或多个正解的存在性%Existence of single and multiple solutions for first order discrete periodic boundary value problems

    Institute of Scientific and Technical Information of China (English)

    许晓婕; 费祥历

    2011-01-01

    The existence principle of single and multiple positive solutions for the first order discrete periodic boundary value problems was studied by employing a fixed point theorem in cones. Based on this principle, the existence of single and multiple positive solutions for the problems was given. Some new results about nonlinear difference equations on a finite discrete segment with periodic boundary conditions were demonstrated.%用一类锥不动点定理首先给出一阶差分周期边值问题的存在性原则,并应用此原则论证了该问题一个或多个正解的存在性,最后通过例证对该问题加以说明.

  15. The Existence of Three Positive Solutions for a Class of Nonlinear Three-Point Boundary Value Problem with ρ-Laplacian%一类具p-Laplace非线性三点边值问题三个正解的存在性

    Institute of Scientific and Technical Information of China (English)

    李相锋; 徐宏武

    2009-01-01

    This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theo- rem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established.

  16. A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation

    Institute of Scientific and Technical Information of China (English)

    Jia-qi Mo; Wan-tao Lin

    2005-01-01

    A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.

  17. A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

    Institute of Scientific and Technical Information of China (English)

    Jia-qi Mo; Wan-tao Lin

    2006-01-01

    A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.

  18. THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    OuyangCheng; MoJiaqi

    2005-01-01

    The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.

  19. Solution of moving boundary problems with implicit boundary condition

    International Nuclear Information System (INIS)

    An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author)

  20. Thick diffusion limit boundary layer test problems

    International Nuclear Information System (INIS)

    We develop two simple test problems that quantify the behavior of computational transport solutions in the presence of boundary layers that are not resolved by the spatial grid. In particular we study the quantitative effects of 'contamination' terms that, according to previous asymptotic analyses, may have a detrimental effect on the solutions obtained by both discontinuous finite element (DFEM) and characteristic-method (CM) spatial discretizations, at least for boundary layers caused by azimuthally asymmetric incident intensities. Few numerical results have illustrated the effects of this contamination, and none have quantified it to our knowledge. Our test problems use leading-order analytic solutions that should be equal to zero in the problem interior, which means the observed interior solution is the error introduced by the contamination terms. Results from DFEM solutions demonstrate that the contamination terms can cause error propagation into the problem interior for both orthogonal and non-orthogonal grids, and that this error is much worse for non-orthogonal grids. This behavior is consistent with the predictions of previous analyses. We conclude that these boundary layer test problems and their variants are useful tools for the study of errors that are introduced by unresolved boundary layers in diffusive transport problems. (authors)

  1. 四元数分析中λ-正则函数向量的带位移边值问题%A class of boundary value problem with shift for λ-regular function vectors in quaternion analysis

    Institute of Scientific and Technical Information of China (English)

    鄢盛勇

    2013-01-01

    A class of boundary value problem with a kind of shit for A- regular function vectors in quaternion analysis is considered. The integral representation of A- regular function vectors, and some integral operators are given. The boundary value problem is transformed into an integral equation problem. Applying integral equation method and the fixed-point theorem, the existence of solution to the problem is proved,and the integral representation of solution is obtained.%研究了四元数分析中λ-正则函数向量的一类带位移的边值问题.首先给出了λ-正则函数向量的积分表示,通过设计积分算子,将此边值问题转化为积分方程问题,借助积分方程理论和不动点原理证明了边值问题解的存在性,并给出了解的积分表达式.

  2. Positive Solutions to Periodic Boundary Value Problems of Second-order Ordinary Differential Equation%二阶常微分方程周期边值问题的正解

    Institute of Scientific and Technical Information of China (English)

    王峰; 崔玉军

    2012-01-01

    非线性二阶周期边值问题可描述天体力学、工程和生物中出现的许多周期现象,其广泛的应用引起了许多学者的关注.本文主要研究二阶周期边值问题正解的存在性,其中非线性项包含一阶导数项.设非线性项满足Caratheodory条件,利用零点指数理论和分析技巧,本文建立了二阶周期边值问题正解的存在性定理,推广并改进了一些已知结果.最后给出一个例子说明主要结果.%Many periodic phenomena in celestial mechanics, engineering and biology can be described as nonlinear second order periodic boundary value problems, whose wide applications have attracted much attention of researchers. We mainly discuss in this paper the existence of positive solutions to the second order periodic boundary value problem, where the nonlinear term involves with the first order derivative. We obtain the existence theorems of the positive solutions to the second order periodic boundary value problem by applying Caratheodory conditions on the nonlinear term and employing the zero point index theory and relevant analysis technique. The results extend and improve known results. Finally, an example is given to illustrate the main results.

  3. A finite difference method for free boundary problems

    KAUST Repository

    Fornberg, Bengt

    2010-04-01

    Fornberg and Meyer-Spasche proposed some time ago a simple strategy to correct finite difference schemes in the presence of a free boundary that cuts across a Cartesian grid. We show here how this procedure can be combined with a minimax-based optimization procedure to rapidly solve a wide range of elliptic-type free boundary value problems. © 2009 Elsevier B.V. All rights reserved.

  4. An inverse problem by boundary element method

    Energy Technology Data Exchange (ETDEWEB)

    Tran-Cong, T.; Nguyen-Thien, T. [University of Southern Queensland, Toowoomba, QLD (Australia); Graham, A.L. [Los Alamos National Lab., NM (United States)

    1996-02-01

    Boundary Element Methods (BEM) have been established as useful and powerful tools in a wide range of engineering applications, e.g. Brebbia et al. In this paper, we report a particular three dimensional implementation of a direct boundary integral equation (BIE) formulation and its application to numerical simulations of practical polymer processing operations. In particular, we will focus on the application of the present boundary element technology to simulate an inverse problem in plastics processing.by extrusion. The task is to design profile extrusion dies for plastics. The problem is highly non-linear due to material viscoelastic behaviours as well as unknown free surface conditions. As an example, the technique is shown to be effective in obtaining the die profiles corresponding to a square viscoelastic extrudate under different processing conditions. To further illustrate the capability of the method, examples of other non-trivial extrudate profiles and processing conditions are also given.

  5. Impulsive Anti-periodic Boundary Value Problem of Nonlinear Fractional Differential Equations%非线性分数阶微分方程脉冲反周期边值问题

    Institute of Scientific and Technical Information of China (English)

    王旭焕; 曾庆红

    2013-01-01

    本文研究q∈(0,1]的分数阶非线性微分方程的脉冲反周期边值问题的解的存在唯一性,我们利用Altman's不动点定理和Leray-Schauder's不动点定理来证明.%In this paper,we prove the existence and uniqueness of solutions for anti-periodic boundary value problem of nonlinear impulsive differential equations of fractional order q ∈ (0,1].Our results are based on Altman's fixed point theorem and Leray-Schauder's fixed point theorem.

  6. Antireflective Boundary Conditions for Deblurring Problems

    Directory of Open Access Journals (Sweden)

    Marco Donatelli

    2010-01-01

    Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.

  7. Numerical Methods for Free Boundary Problems

    CERN Document Server

    1991-01-01

    About 80 participants from 16 countries attended the Conference on Numerical Methods for Free Boundary Problems, held at the University of Jyviiskylii, Finland, July 23-27, 1990. The main purpose of this conference was to provide up-to-date information on important directions of research in the field of free boundary problems and their numerical solutions. The contributions contained in this volume cover the lectures given in the conference. The invited lectures were given by H.W. Alt, V. Barbu, K-H. Hoffmann, H. Mittelmann and V. Rivkind. In his lecture H.W. Alt considered a mathematical model and existence theory for non-isothermal phase separations in binary systems. The lecture of V. Barbu was on the approximate solvability of the inverse one phase Stefan problem. K-H. Hoff­ mann gave an up-to-date survey of several directions in free boundary problems and listed several applications, but the material of his lecture is not included in this proceedings. H.D. Mittelmann handled the stability of thermo capi...

  8. BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE

    Institute of Scientific and Technical Information of China (English)

    DONG Zheng-zhu; LI Shun-cai; YU De-hao

    2005-01-01

    By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.

  9. Solvability of a (p, n-p-type multi-point boundary-value problem for higher-order differential equations

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2003-12-01

    Full Text Available In this article, we study the differential equation $$ (-1^{n-p} x^{(n}(t=f(t,x(t,x'(t,dots,x^{(n-1}(t, $$ subject to the multi-point boundary conditions $$displaylines{ x^{(i}(0=0 quad hbox{for }i=0,1,dots,p-1,cr x^{(i}(1=0 quad hbox{for }i=p+1,dots,n-1,cr sum_{i=1}^malpha_ix^{(p}(xi_i=0, }$$ where $1le ple n-1$. We establish sufficient conditions for the existence of at least one solution at resonance and another at non-resonance. The emphasis in this paper is that $f$ depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.

  10. The Unique Solution for Periodic Boundary Value Problems of the Discontinuous Second Order Nonlinear Differential Equations%不连续二阶非线性微分方程的周期边值问题的唯一解

    Institute of Scientific and Technical Information of China (English)

    王李

    2006-01-01

    The existence of the unique solution for periodic boundary value problems of the discontinuous second order nonlinear differential equations in Banach spaces is presented. Under quite weakly conditions, we show that the unique solution of the above problems can be obtained by the uniformly limit of an iterative sequence. Moreover,the error estimate of the iterative sequences of approximation solutions is given.%在Banach中,本文在很弱条件下,通过迭代序列得到了不连续二阶非线性微分方程的周期边值问题的唯一解存在性的一个充分条件,而且给出了迭代序列近代解的误差估计.

  11. Upscaling in Diffusion Problems in Domains with Semipermeable Boundaries

    International Nuclear Information System (INIS)

    The asymptotic behavior of the solutions of some nonlinear variational inequalities with highly oscillating coefficients modeling chemical reactive flows through the exterior of a domain containing periodically distributed reactive solid obstacles, with period ε, is analyzed. In this kind of boundary value problems there are involved two distinct sources of oscillations, one coming from the geometrical structure of the domain and the other from the fact that the medium is heterogeneous. We focus on the only case in which a real interaction between both these sources appears, i.e. the case in which the obstacles are of the so-called critical size and we prove that the solution of such a boundary-value problem converges to the solution of a new problem, associated to an operator which is the sum of a standard homogenized one and extra zero order terms coming from the geometry and the nonlinearity of the problem. (author)

  12. On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at a point

    Directory of Open Access Journals (Sweden)

    Rutkauskas Stasys

    2011-01-01

    Full Text Available Abstract A system of elliptic equations which are irregularly degenerate at an inner point is considered in this article. The equations are weakly coupled by a matrix that has multiple zero eigenvalue and corresponding to it adjoint vectors. Two statements of a well-posed Dirichlet type problem in the class of smooth functions are given and sufficient conditions on the existence and uniqueness of the solutions are obtained.

  13. Finite temperature expectation values of boundary operators

    OpenAIRE

    Takacs, G.

    2008-01-01

    A conjecture is presented for the thermal one-point function of boundary operators in integrable boundary quantum field theories in terms of form factors. It is expected to have applications in studying boundary critical phenomena and boundary flows, which are relevant in the context of condensed matter and string theory. The conjectured formula is verified by a low-temperature expansion developed using finite size techniques, which can also be used to evaluate higher point functions both in ...

  14. A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems

    Directory of Open Access Journals (Sweden)

    Ghasem Alizadeh Afrouzi

    2006-10-01

    Full Text Available In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem $$displaylines{ -u''(x+m(xu(x =lambda f(x,u(x,quad xin (a,b,cr u(a=u(b=0, }$$ where $lambda>0$, $f:[a,b]imes mathbb{R}o mathbb{R}$ is a continuous function which changes sign on $[a,b]imes mathbb{R}$ and $m(xin C([a,b]$ is a positive function.

  15. Finite temperature expectation values of boundary operators

    Energy Technology Data Exchange (ETDEWEB)

    Takacs, G. [HAS Research Group for Theoretical Physics, H-1117 Budapest, Pazmany Peter setany 1/A (Hungary)], E-mail: takacs@elte.hu

    2008-12-21

    A conjecture is presented for the thermal one-point function of boundary operators in integrable boundary quantum field theories in terms of form factors. It is expected to have applications in studying boundary critical phenomena and boundary flows, which are relevant in the context of condensed matter and string theory. The conjectured formula is verified by a low-temperature expansion developed using finite size techniques, which can also be used to evaluate higher point functions both in the bulk and on the boundary.

  16. 二阶及2n阶周期边值问题的多个正解%Multiple positive solutions of second-order and 2nth-order periodic boundary value problems

    Institute of Scientific and Technical Information of China (English)

    戚仕硕; 马海霞

    2011-01-01

    应用Leggett-Williams不动点定理及其推论研究二阶微分方程周边值问题,并在较有关文献更弱的条件下分别证明了其至少有三个或至少有两个正解的存在性结果.使用相同的理论方法讨论了一类2n阶微分方程周期边值问题,同样获得了其至少有三个或至少有两个正解的存在性定理.论文所得结论在一定程度上推广和改进了所引用相关文献中的一些结果.%In the first place,we investigate in this article the periodic boundary value problems for second-order differential equations by an application of Leggett-Williams' Fixed Point Theorem and its corollary,and prove under much weaker conditions than those used in the cited literature the existence results of at least three or at least two positive solutions to the problems studied,respectively.Secondly,we utilize the same theoretical approaches to discuss a family of periodic boundary value problems for 2nth-order differential equations and obtain the similar existence theorems on their possessing at least three or at least two positive solutions.At last,we should point out that all the results gained here generalize and develop to some extent those ones in the relevant literature cited herein.

  17. A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation

    Institute of Scientific and Technical Information of China (English)

    SUNJian-she; YELiu-qing

    2003-01-01

    Using the second Green formula, the boundary problem of Laplace equation satisfied by potential function of static electric field is transformed to the problem of the boundary integral equation,and then a boundary integral equation approach is established by partitioning boundary using linear boundary element.

  18. Reduction of the Dirichlet problem to an initial value problem.

    Science.gov (United States)

    Kalaba, R.; Ruspini, E. H.

    1971-01-01

    Although the derivation is concerned with solutions for plane regions with prescribed boundary values, the approach presented could by easily generalized to higher dimensions. The initial-value method is derived by a combination of invariant imbedding techniques and the Fredholm integral equation method of representation of the potential as a function of a dilayer distribution on the boundary of the region in question.

  19. Dirichlet boundary value problem with variable growth

    Institute of Scientific and Technical Information of China (English)

    董增福; 付永强

    2004-01-01

    In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of W'n,p(χ) spaces by means of an abstract result for variational inequalities obtained by Gossez and Mustonen. Our result generalizes the corresponding one of Kovacik and Rakosntk.

  20. The Initial Boundary Value Problem of a Class of Diffusion Equations and Its Application%一类扩散方程的初边值问题及其应用

    Institute of Scientific and Technical Information of China (English)

    谈骏渝

    2012-01-01

    对一类扩散方程的初边值问题给出了以球贝塞尔函数表示的级数解,由此得到了裂变产物在燃料芯块中扩散问题的解以及裂变产物扩散的释放速度,为有效开展对裂变产物的扩散过程及反应堆燃料元件破损探测信号的定量分析提供了条件.%A series solution expressed by the Bessel function is given to the initial boundary value problems of a class of diffusion equations.Hence,the solutions to the proliferation problems of fission products in the fuel pellets and their release rates are obtained,thus providing necessary conditions for the quantitative analysis of the diffusion process of fission products and the detection of the signals of the reactor fuel element's damage.

  1. Green's function of a heat problem with a periodic boundary condition

    Science.gov (United States)

    Erzhanov, Nurzhan E.

    2016-08-01

    In the paper, a nonlocal initial-boundary value problem for a non-homogeneous one-dimensional heat equation is considered. The domain under consideration is a rectangle. The classical initial condition with respect to t is put. A nonlocal periodic boundary condition by a spatial variable x is put. It is well-known that a solution of problem can be constructed in the form of convergent orthonormal series according to eigenfunctions of a spectral problem for an operator of multiple differentiation with periodic boundary conditions. Therefore Green's function can be also written in the form of an infinite series with respect to trigonometric functions (Fourier series). For classical first and second initial-boundary value problems there also exists a second representation of the Green's function by Jacobi function. In this paper we find the representation of the Green's function of the nonlocal initial-boundary value problem with periodic boundary conditions in the form of series according to exponents.

  2. Elasticity problems in domains with nonsmooth boundaries

    International Nuclear Information System (INIS)

    In the present work we study the behaviour of elastic stress fields in domains with non-regular boundaries. We consider three-dimensional problems in elastic media with thin conical defects (inclusions or cavities) and analyse the stress singularity at their vertices. To construct asymptotic expansions for the stress and displacement fields in terms of a small parameter ε related to the 'thickness' of the defect, we employ a technique based on the work by Kondrat'ev, Maz'ya, Nazarov and Plamenevskii. We first study the stress distribution in an elastic body with a thin conical notch. We derive an asymptotic representation for the stress singularity exponent by reducing the original problem to a spectral problem for a 9x9 matrix. The elements of this matrix are found to depend upon the geometry of the cross-section of the notch and the elastic properties of the medium. We specify the sets of eigenvalues and the corresponding eigenvectors for a circular, elliptical, 'triangular' and 'square' cross-section, and show that the strongest singularity is associated with the 'triangular' cross-section, and is generated by a non-axisymmetric load. We then analyse the stress distribution near a thin conical inclusion which is allowed to slide freely along its axis. We derive the representation for the stress singularity exponent for the case of a circular conical inclusion whose elastic properties differ from those of the medium. In the last chapter we study the stress distribution in the vicinity of a thin 'coated' conical inclusion. We show that a soft thin coating (perfectly bonded to the inclusion and the surrounding material) can be replaced by a so-called linear interface at which the normal displacement is discontinuous, and the stresses are proportional to the 'jump' in the normal displacement across the coating. We analyse the effect of the properties of the coating on the stress singularity exponent and compare the results with those for a perfectly bonded

  3. A Non-Iterative Transformation Method for Newton's Free Boundary Problem

    OpenAIRE

    Fazio, Riccardo

    2013-01-01

    In book II of Newton's "Principia Mathematica" of 1687 several applicative problems are introduced and solved. There, we can find the formulation of the first calculus of variations problem that leads to the first free boundary problem of history. The general calculus of variations problem is concerned with the optimal shape design for the motion of projectiles subject to air resistance. Here, for Newton's optimal nose cone free boundary problem, we define a non-iterative initial value method...

  4. An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions

    Directory of Open Access Journals (Sweden)

    Cabada Alberto

    2011-01-01

    Full Text Available The aim of this paper is to point out recent and classical results related with the existence of solutions of second-order problems coupled with nonlinear boundary value conditions.

  5. Analysis of Blasius Equation for Flat-Plate Flow with Infinite Boundary Value

    DEFF Research Database (Denmark)

    Miansari, M. O.; Miansari, M. E.; Barari, Amin; Domairry, G.

    2010-01-01

    and write the nonlinear differential equation in the state space format, and then solve the initial value problem instead of boundary value problem. The significance of linear part is a key factor in convergence. A first seen linear part may lead to an unstable solution, therefore an extra term is...

  6. A free boundary problem for fluid flow through porous media

    OpenAIRE

    Di Nucci, Carmine

    2015-01-01

    This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The problem solution is obtained by using an approximate model which provides the analytical expression for the free boundary profile. Within the range of validity of the model assumptions, the computational results show agreement with data in literature.

  7. THE NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH A BOUNDARY PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    Jingsun Yao; Jiaqi Mo

    2005-01-01

    The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.

  8. A CLASS OF NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

    Institute of Scientific and Technical Information of China (English)

    MO Jia-qi; WANG Hui; LIN Wan-tao

    2005-01-01

    A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.

  9. WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

    Institute of Scientific and Technical Information of China (English)

    V. S. Guliyev; Zhijian Wu

    2005-01-01

    We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.

  10. Solution of a Problem Linear Plane Elasticity with Mixed Boundary Conditions by the Method of Boundary Integrals

    Directory of Open Access Journals (Sweden)

    Nahed S. Hussein

    2014-01-01

    Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of …eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.

  11. The Solution of A Compound Periodic Boundary Problem

    Institute of Scientific and Technical Information of China (English)

    ZHU Jun-ming; DU Jin-yuan

    2005-01-01

    We have studied the compound periodic boundary problem in the upper half plane above the real axis. Under proper conditions, we obtain a periodic and sectionally holomorphic function in the upper half plane. In addition, we have also solved the compound boundary problem with discontinuities of the first kind of the coefficients in the Hilbert condition.

  12. On correct boundary conditions for the Asian option pricing problem

    International Nuclear Information System (INIS)

    The problem of finding the price of the Asian option has been analyzed. The main goal is to construct a well-posed mathematical problem. Modified boundary conditions obtained by projecting the original equation on the boundary of the domain under consideration have been proposed

  13. A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION

    Institute of Scientific and Technical Information of China (English)

    Xie Feng

    2003-01-01

    The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.

  14. Boundary value problemfor multidimensional fractional advection-dispersion equation

    Directory of Open Access Journals (Sweden)

    Khasambiev Mokhammad Vakhaevich

    2015-05-01

    Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

  15. Spectral analysis of nonselfadjoint Schr(o)dinger problem with eigenparameter in the boundary condition

    Institute of Scientific and Technical Information of China (English)

    M.Yakit ONGUN

    2007-01-01

    In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.

  16. Spectral analysis of nonselfadjoint Schrdinger problem with eigenparameter in the boundary condition

    Institute of Scientific and Technical Information of China (English)

    M.Yakit; ONGUN

    2007-01-01

    In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given.

  17. The Existence of Positive Solutions for Third-Order -Laplacian -Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales

    OpenAIRE

    Xu Fuyi; Meng Zhaowei

    2009-01-01

    We study the following third-order -Laplacian -point boundary value problems on time scales , , , , , where is -Laplacian operator, that is, , , , . We obtain the existence of positive solutions by using fixed-point theorem in cones. In particular, the nonlinear term is allowed to change sign. The conclusions in this paper essentially extend and improve the known results.

  18. Numerical Computing for a Class of Free Multipoint Boundary Value Problem of O. D. E in the Intervention of Exchange Rate%汇率干预中的多点自由边值问题的数值计算方法

    Institute of Scientific and Technical Information of China (English)

    赵连霞; 朱正佑; 秦成林

    2005-01-01

    In this paper by means of generalized shooting method and homotopy technique a numerical method was given for computing free multipoint boundary value problem proposed in the intervention of exchange rate by Cadenillas and Fernando Zapatero. A numerical example was given for illustrating the validity of this method.

  19. Diagonal Pade approximations for initial value problems

    International Nuclear Information System (INIS)

    Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab

  20. Diagonal Pade approximations for initial value problems

    Energy Technology Data Exchange (ETDEWEB)

    Reusch, M.F.; Ratzan, L.; Pomphrey, N.; Park, W.

    1987-06-01

    Diagonal Pade approximations to the time evolution operator for initial value problems are applied in a novel way to the numerical solution of these problems by explicitly factoring the polynomials of the approximation. A remarkable gain over conventional methods in efficiency and accuracy of solution is obtained. 20 refs., 3 figs., 1 tab.

  1. Boundary values as Hamiltonian variables: new Poisson brackets

    International Nuclear Information System (INIS)

    It is shown that the standard Poisson brackets in field theory can be modified by adding some surface terms. The definition of the Poisson brackets permits to treat boundary values of a field on equal footing with its internal values and directly estimate the brackets between both surface and volume integrals. 8 refs

  2. Solution of Exterior Acoustic Problems by the Boundary Element Method.

    Science.gov (United States)

    Kirkup, Stephen Martin

    Available from UMI in association with The British Library. The boundary element method is described and investigated, especially in respect of its application to exterior two -dimensional Laplace problems. Both empirical and algebraic analyses (including the effects of approximation of the boundary and boundary functions and the precision of the evaluation of the discrete forms) are developed. Methods for the automatic evaluation of the discrete forms of the Laplace and Helmholtz integral operators are reviewed and extended. Boundary element methods for the solution of exterior Helmholtz problems with general (but most importantly Neumann) boundary conditions are reviewed and some are explicitly stated using a new notation. Boundary element methods based on the boundary integral equations introduced by Brakhage & Werner/ Leis/ Panich/ Kussmaul (indirect) and Burton & Miller (direct) are given prime consideration and implemented for three -dimensional problems. The influence of the choice of weighting parameter on the performance of the methods is explored and further guidance is given. The application of boundary element methods and methods based on the Rayleigh integral to acoustic radiation problems are considered. Methods for speeding up their solution via the boundary element method are developed. Library subroutines for the solution of acoustic radiation problems are described and demonstrated. Computational techniques for the problem of predicting the noise produced by a running engine are reviewed and appraised. The application of the boundary element method to low-noise engine design and in the design of noise shields is considered. The boundary element method is applied to the Ricardo crankcase simulation rig, which is an engine -like structure. A comparison of predicted and measured sound power spectra is given.

  3. Boundary integral equation methods in eigenvalue problems of elastodynamics and thin plates

    CERN Document Server

    Kitahara, M

    1985-01-01

    The boundary integral equation (BIE) method has been used more and more in the last 20 years for solving various engineering problems. It has important advantages over other techniques for numerical treatment of a wide class of boundary value problems and is now regarded as an indispensable tool for potential problems, electromagnetism problems, heat transfer, fluid flow, elastostatics, stress concentration and fracture problems, geomechanical problems, and steady-state and transient electrodynamics.In this book, the author gives a complete, thorough and detailed survey of the method. It pro

  4. Complexity of valued constraint satisfaction problems

    CERN Document Server

    Živný, Stanislav

    2012-01-01

    The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions over all variables. This fundamental research problem has been studied within several different contexts of discrete mathematics, computer science and artificial intelligence under different names: Min-Sum problems, MAP inference in Markov random fields (MRFs) and conditional random fields (CRFs), Gibbs energy minimisation, valued constraint satisfaction problems (VCSPs), and, for two-state variabl

  5. A qualitative theory for parabolic problems under dynamical boundary conditions

    Directory of Open Access Journals (Sweden)

    von Bellow Joachim

    2000-01-01

    Full Text Available For nonlinear parabolic problems in a bounded domain under dynamical boundary conditions, general comparison techniques are established similar to the ones under Neumann or Dirichlet boundary conditions. In particular, maximum principles and basic a priori estimates are derived, as well as lower and upper solution techniques that lead to functional band type estimates for classical solutions. Finally, attractivity properties of equilibria are discussed that also illustrate the damping effect of the dissipative dynamical boundary condition.

  6. A Duality Approach for the Boundary Variation of Neumann Problems

    DEFF Research Database (Denmark)

    Bucur, Dorin; Varchon, Nicolas

    2002-01-01

    In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....

  7. A duality approach or the boundary variation of Neumann problems

    DEFF Research Database (Denmark)

    Bucur, D.; Varchon, Nicolas

    2002-01-01

    In two dimensions, we study the stability of the solution of an elliptic equation with Neumann boundary conditions for nonsmooth perturbations of the geometric domain. Using harmonic conjugates, we relate this problem to the shape stability of the solution of an elliptic equation with Dirichlet...... boundary conditions. As a particular case, we prove the stability of the solution under a topological constraint ( uniform number of holes), which is analogous to Sverak's result for Dirichlet boundary conditions....

  8. APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS

    OpenAIRE

    Vorona Yu.V.; Kara I.D.

    2015-01-01

    Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.

  9. Moving boundaries in heat conduction and mass diffusion problems

    International Nuclear Information System (INIS)

    A brief introduction to the mathematical study of moving boundaries in heat-conduction and mass-diffusion problems is presented. A list of references is given for further investigation of the analytical and numerical methods mentioned in the text

  10. APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS

    Directory of Open Access Journals (Sweden)

    Vorona Yu.V.

    2015-12-01

    Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.

  11. Parametrices and exact paralinearization of semi-linear boundary problems

    DEFF Research Database (Denmark)

    Johnsen, Jon

    2008-01-01

    The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization. The...... homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....

  12. Parametrices and exact paralinearisation of semi-linear boundary problems

    DEFF Research Database (Denmark)

    Johnsen, Jon

    The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearisation. The...... homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation....

  13. A Free Boundary Problem in the Theory of the Stars

    CERN Document Server

    Yazadjiev, S S; Todorov, M D; Fiziev, P P

    2000-01-01

    We investigate numerically models of the static spherically symmetric boson-fermion stars in the scalar-tensor theory of gravity with massive dilaton field. The proper mathematical model of such stars is interpreted as a nonlinear two-parametric eigenvalue problem with unknown internal boundary. To solve this problem the Continuous Analogue of Newton Method is used.

  14. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  15. Test set for initial value problem solvers

    OpenAIRE

    Lioen, W.M.; Swart, de, Jacques

    1998-01-01

    The CWI test set for IVP solvers presents a collection of Initial Value Problems to test solvers for implicit differential equations. This test set can both decrease the effort for the code developer to test his software in a reliable way, and cross the bridge between the application field and numerical mathematics. This document contains the descriptive part of the test set. It describes the test problems and their origin, and reports on the behavior of a few state-of-the-art solvers on thes...

  16. Vector-valued measure and the necessary conditions for the optimal control problems of linear systems

    International Nuclear Information System (INIS)

    The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)

  17. Boundary element analysis of nonlinear transient heat conduction problems

    International Nuclear Information System (INIS)

    In this paper, the theory of the BEM applied to transient heat-conduction problems is reviewed. New time marching schemes which are based upon full boundary integrals without excessive use of large matrices, are introduced. An algorithm for dealing with the nonlinear boundary condition of radiation is described. An accuracy measure which deals with the singularities in fundamental solution parameters is discussed. A number of case studies with different geometrical shapes and different loading and boundary conditions were analyzed using the developed techniques, and the results were compared with corresponding analytical solutions and/or finite element results. It is clear that the developed boundary element procedure is more accurate and efficient than the finite element method for the analysis of such problems. (author)

  18. Well Posed Problems and Boundary Conditions in Computational Fluid Dynamics

    OpenAIRE

    Nordström, Jan

    2015-01-01

    All numerical calculations will fail to provide a reliable answer unless the continuous problem under consideration is well posed. Well-posedness depends in most cases only on the choice of boundary conditions. In this paper we will highlight this fact by discussing well-posedness of the most important equations in computational uid dynamics, namely the time-dependent compressible Navier-Stokes equations.   In particular, we will discuss i) how many boundary conditions are required, ii) where...

  19. Inhomogeneous inflation: The initial-value problem

    Energy Technology Data Exchange (ETDEWEB)

    Laguna, P. (Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico (USA)); Kurki-Suonio, H. (Lawrence Livermore National Laboratory, University of California, Livermore, California (USA)); Matzner, R.A. (Center for Relativity, The University of Texas at Austin, Austin, Texas (USA))

    1991-11-15

    We present a spatially three-dimensional study for solving the initial-value problem in general relativity for inhomogeneous cosmologies. We use York's conformal approach to solve the constraint equations of Einstein's field equations for scalar field sources and find the initial data which will be used in the evolution. This work constitutes the first stage in the development of a code to analyze the effects of matter and spacetime inhomogeneities on inflation.

  20. Optimal control problems for impulsive systems with integral boundary conditions

    Directory of Open Access Journals (Sweden)

    Allaberen Ashyralyev

    2013-03-01

    Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

  1. Exact and Truncated Difference Schemes for Boundary Value ODEs

    CERN Document Server

    Gavrilyuk, Ivan P; Makarov, Volodymyr L; Kutniv, Myroslav V

    2011-01-01

    The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in

  2. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

    Directory of Open Access Journals (Sweden)

    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  3. A Computational Study of the Boundary Value Methods and the Block Unification Methods for y″=f(x,y,y′)

    OpenAIRE

    Biala, T. A.

    2016-01-01

    We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency.

  4. Weak solutions for an initial-boundary Q-Tensor problem related to liquid crystals

    OpenAIRE

    Guillén González, Francisco Manuel; Rodríguez Bellido, María Ángeles

    2015-01-01

    The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet boundary conditions for the velocity u and either nonhomogeneous Dirichlet or homogeneous Neumann boundary conditions for the tensor Q. The corresponding initial-value problem in the whole space R3 was analyzed in [Paicu & Zarnescu, 2012]. In this paper, three main results concerning weak solutions will be proved; the existence of global in time weak solutions (bounded...

  5. Artificial boundary conditions for axisymmetric eddy current probe problems

    OpenAIRE

    Haddar, Houssem; Jiang, Zixian; Lechleiter, Armin

    2015-01-01

    We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as th...

  6. Bibliography on moving boundary problems with key word index

    International Nuclear Information System (INIS)

    This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included

  7. Bibliography on moving boundary problems with key word index

    Energy Technology Data Exchange (ETDEWEB)

    Wilson, D.G.; Solomon, A.D.; Trent, J.S.

    1979-10-01

    This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included. (RWR)

  8. Existence and Regularity for Boundary Cauchy Problems with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Jung-Chan Chang

    2014-01-01

    Full Text Available The aim of this work is to investigate a class of boundary Cauchy problems with infinite delay. We give some sufficient conditions ensuring the uniqueness, existence, and regularity of solutions. For illustration, we apply the result to an age dependent population equation, which covers some special cases considered in some recent papers.

  9. Existence and Regularity for Boundary Cauchy Problems with Infinite Delay

    OpenAIRE

    Jung-Chan Chang

    2014-01-01

    The aim of this work is to investigate a class of boundary Cauchy problems with infinite delay. We give some sufficient conditions ensuring the uniqueness, existence, and regularity of solutions. For illustration, we apply the result to an age dependent population equation, which covers some special cases considered in some recent papers.

  10. Mathematical modeling of moving boundary problems in thermal energy storage

    Science.gov (United States)

    Solomon, A. D.

    1980-01-01

    The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

  11. Free Boundary Problem of Ono—steady State Seepage Flow

    Institute of Scientific and Technical Information of China (English)

    XiaomingGUO; Ying-SUN; 等

    1999-01-01

    Along with the vigorous developing construction,the number of various underground engineerings is greatly increasing,Such as:the foundations of dams and high-rise multistoried houses,subways and tunnels,water and oil wells etc., where the close attention is always payed to the seepage behaviour in the media around the strutures.The Variatonal Inequality formulation and its FEM solution for the free boundary problem of 2D steady state seepage flow was given by the authors,In this paper a further investigation is made on the non-steady state seepage problem,taken the seepage flow of wells as an example.The presented approach-Variational Inequality and its FEM solution-is also very beneficial to the non-steady state problems,where the transient free boundary can also be defined directly without conventional iterations.

  12. Free Boundary Problems for a Lotka-Volterra Competition System

    Science.gov (United States)

    Wang, Mingxin; Zhao, Jingfu

    2014-09-01

    In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free boundary. We prove a spreading-vanishing dichotomy, namely the two species either successfully spread to the entire space as time t goes to infinity and survive in the new environment, or they fail to establish and die out in the long run. The long time behavior of the solutions and criteria for spreading and vanishing are also obtained. This paper is an improvement and extension of J. Guo and C. Wu.

  13. Global Behavior of the Components for the Second Order -Point Boundary Value Problems

    OpenAIRE

    An Yulian; Ma Ruyun

    2008-01-01

    Abstract We consider the nonlinear eigenvalue problems , , , , where , , and for , with ; ; . There exist two constants such that and , . Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.

  14. Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems

    Science.gov (United States)

    Ivanyshyn Yaman, Olha; Le Louër, Frédérique

    2016-09-01

    This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.

  15. Existence of Solutions for a Class of Anti-periodic Boundary Value Problems with Fractional q-Difference Equations%一类反周期分数阶 q-差分边值问题解的存在性

    Institute of Scientific and Technical Information of China (English)

    孙明哲; 侯成敏

    2014-01-01

    利用基本的不动点定理研究一类带有反周期非线性分数阶 q-差分方程边值问题,得到了边值问题解的存在与唯一的充分条件,并通过具体方程验证了所得结论。%We studied a class of the fractional q-differences boundary value problem with the fractional q-differences boundary conditions with the aid of some standard fixed point theorems,obtaining sufficient conditions for the existence and uniqueness results of solutions.As the application,some equations were presented to illustrate the main results.

  16. Free boundary problems in PDEs and particle systems

    CERN Document Server

    Carinci, Gioia; Giardinà, Cristian; Presutti, Errico

    2016-01-01

    In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases. All the models discussed in this volume have an interest in problems arising in several research fields...

  17. The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves

    OpenAIRE

    Kreiss, H.; Winicour, J.

    2010-01-01

    The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the worldtube. We establish the well-posedness of this problem for the evolution of a quasilinear scalar wave by means of energy estimates. The treatment is given in characteristic coordinates and thus provides a guide for developing stable finite difference algori...

  18. An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

    Science.gov (United States)

    Alam Khan, Najeeb; Razzaq, Oyoon Abdul

    2016-03-01

    In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

  19. 一类半正定二阶周期边值问题的正解%Positive Solutions to A Kind of Semipositone Second-Order Periodic Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    田颖辉

    2015-01-01

    In this paper,the positive solutions to semipositone superlinear singulare quations with peri-odic boundary conditions are studied,the proof relies on Krasnoselskii fixed point theorem on compression and expansion of cones.%研究半正定条件下奇异超线性二阶周期边值问题,利用锥不动点定理给出一类奇异半正定二阶周期边值问题正解的存在性。

  20. On the Existence and Uniqueness of Rv-Generalized Solution for Dirichlet Problem with Singularity on All Boundary

    Directory of Open Access Journals (Sweden)

    V. Rukavishnikov

    2014-01-01

    Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.

  1. Axis Problem of Rough 3-Valued Algebras

    Institute of Scientific and Technical Information of China (English)

    Jianhua Dai; Weidong Chen; Yunhe Pan

    2006-01-01

    The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.

  2. System, Subsystem, Hive: Boundary Problems in Computational Theories of Consciousness

    Science.gov (United States)

    Fekete, Tomer; van Leeuwen, Cees; Edelman, Shimon

    2016-01-01

    A computational theory of consciousness should include a quantitative measure of consciousness, or MoC, that (i) would reveal to what extent a given system is conscious, (ii) would make it possible to compare not only different systems, but also the same system at different times, and (iii) would be graded, because so is consciousness. However, unless its design is properly constrained, such an MoC gives rise to what we call the boundary problem: an MoC that labels a system as conscious will do so for some—perhaps most—of its subsystems, as well as for irrelevantly extended systems (e.g., the original system augmented with physical appendages that contribute nothing to the properties supposedly supporting consciousness), and for aggregates of individually conscious systems (e.g., groups of people). This problem suggests that the properties that are being measured are epiphenomenal to consciousness, or else it implies a bizarre proliferation of minds. We propose that a solution to the boundary problem can be found by identifying properties that are intrinsic or systemic: properties that clearly differentiate between systems whose existence is a matter of fact, as opposed to those whose existence is a matter of interpretation (in the eye of the beholder). We argue that if a putative MoC can be shown to be systemic, this ipso facto resolves any associated boundary issues. As test cases, we analyze two recent theories of consciousness in light of our definitions: the Integrated Information Theory and the Geometric Theory of consciousness. PMID:27512377

  3. Mixed Boundary Problem for the Traversable Wormhole Models

    OpenAIRE

    Konstantinov, M. Yu.

    1997-01-01

    The conditions of the traversable wormhole joining with the exterior space-time are considered in details and the mixed boundary problem for the Einstein equations is formulated. It is shown that, in opposite to some declarations, the conditions of the wormhole joining with the exterior space-time have non-dynamical nature and can not be defined by the physical processes. The role of these conditions in the formation of the causal structure of space-time is analyzed. It is shown that the caus...

  4. A Dynamic Boundary Guarding Problem with Translating Targets

    OpenAIRE

    Smith, Stephen L.; Bopardikar, Shaunak D.; Bullo, Francesco

    2009-01-01

    We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the...

  5. Lean Knowledge Management: The Problem of Value

    OpenAIRE

    Rooke, John; Sapountzis, Stelios; Koskela, Lauri; Codinhoto, Ricardo; Kagioglou, Mike

    2010-01-01

    Lean knowledge management is defined here as: getting the right information, in the right form, to the right people at the right time. This definition highlights series of practical problems for knowledge management in the built environment which, in turn, have implications for lean theory. In the terms of TFV theory, the problems that arise from getting information to the right people at the right time are essentially flow (F) issues, but those that are concerned with defin...

  6. Boundary conditions for free surface inlet and outlet problems

    KAUST Repository

    Taroni, M.

    2012-08-10

    We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.

  7. SECOND-ORDER ANALYSIS OF A BOUNDARY CONTROL PROBLEM FOR THE VISCOUS CAHN–HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITION

    Directory of Open Access Journals (Sweden)

    Pierluigi Colli

    2015-07-01

    Full Text Available In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn–Hilliard equation with possibly singular potentials and dynamic boundary conditions.

  8. Special extreme value problems and extremum principles

    Science.gov (United States)

    Schröer, H.

    2002-08-01

    The first part of this book are special extremum problems that are interesting for specialist papers. The book begins with the calculating of extremum angles. Then a triangle in a pair of scissors is viewed. There are a simple and a more complicated model. The next section contains a kite that can be presented with a foot-rule. In the second part different extremum problems with side conditions are treated. The side conditions are chosen most general. Then the differentiation of the target function is set equal to zero. In the midpoint is the form of these necessary conditions of local extrema. Triangles, trapezoids, prisms, 5-gons described with one or two functions belong to the program. Necessary conditions of extremum areas and perimeters are searched. There is an english and a german edition.

  9. 探讨蒙特卡罗方法在解微分方程边值问题中的应用%On the Application of Monte Carlo Method in Solving the Problem of Boundary Value of Differential Equation

    Institute of Scientific and Technical Information of China (English)

    冉营丽

    2015-01-01

    Monte Carlo Method, abbreviated as MC, is also called statistical simulation method. It was first put forward in 1940s by S. M. Ulam and J. V. Neumann, participants of the "Manhattan Project" which aimed at the development of atomic bomb in the World II. Later, mathematicians named it Monte Carlo Method. It is a very important statistical method which, under the guidance of probability theory, is used to solve various computing problems by means of pseudo-random numbers and it is widely used in the fields of financial engineering, macro-economics, computational physics, etc. In the 18th century, Buffon, a French mathematician, used the needle-test method to calculateπ, the PI, which is considered the beginning of applying Monte Carlo Method.%蒙特·卡罗方法(Monte Carlo method),也称统计模拟方法,简写MC。是由20世纪40年代美国在第二次世界大战中研制原子弹的“曼哈顿计划”中的计划成员S.M.乌拉姆和J.冯·诺伊曼首先提出。之后数学家将其命名为蒙特卡罗,它以概率理论为指导,是一种非常重要的统计方法,利用常见的伪随机数解决多种计算问题的方法。这种方法在金融工程学、宏观经济学、计算物理学等领域被广泛的应用。早在18世纪法国数学家布丰利用投针实验的方法求圆周率π,被认为是蒙特·卡罗方法的起源。

  10. On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control

    International Nuclear Information System (INIS)

    In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.

  11. Expectation values in relativistic Coulomb problems

    Energy Technology Data Exchange (ETDEWEB)

    Suslov, Sergei K, E-mail: sks@asu.ed [School of Mathematical and Statistical Sciences and Mathematical, Computational, and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804 (United States)

    2009-09-28

    We evaluate the matrix elements (Or{sup p}), where O = {l_brace}, {beta},i{alpha}n{beta}{r_brace} are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions {sub 3}F{sub 2}(1) for all suitable powers. Their connections with the Chebyshev and Hahn polynomials of a discrete variable are emphasized. As a result, we derive two sets of Pasternack-type matrix identities for these integrals, when p -> -p - 1 and p -> -p - 3, respectively. Some applications to the theory of hydrogenlike relativistic systems are reviewed.

  12. Boundary element method approach to magnetostatic wave problems

    Science.gov (United States)

    Yashiro, K.; Ohkawa, S.; Miyazaki, M.

    1985-03-01

    In this paper, the technique for application of the boundary element method (BEM) to analysis of magnetostatic waves (MSWs) is established. To show the availability of the technique, two types of waveguides for the MSW are studied; one is a waveguide constituting a YIG slab shielded with metal plates and the other is a waveguide consisting of an unshielded YIG slab. With the former structure the results obtained by the present technique are compared with the analytical solutions, and with the latter the BEM is compared with Marcatili's approximate method since there is no analytical solution in this case. Those comparisons are performed successfully for both cases. The paper concludes that the BEM is useful and effective for analysis of a wide range of MSW problems.

  13. Adaptive Boundary Elements and Error Estimation for Elastic Problems

    Directory of Open Access Journals (Sweden)

    Jingguo Qu

    2014-02-01

    Full Text Available In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process of H-R adaptive refinement, the solution error was estimated by the interpolation residue. In addition, this method is easy to programming, which is carried out in the program by automatically creating new adaptive data files. Then a great deal of fore-disposal and post-disposal can be saved. Its validity and effectiveness have been confirmed by numerical example

  14. A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

    OpenAIRE

    Nordström, Jan; Abbas, Qaisar; Erickson, Brittany A.; Frenander, Hannes

    2014-01-01

    A new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary...

  15. Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions

    Directory of Open Access Journals (Sweden)

    Chuanzhi Bai

    2007-05-01

    Full Text Available We are concerned with the nonlinear second-order impulsive periodic boundary value problem u''(t=f(t,u(t,u'(t, t∈[0,T]∖{t1}, u(t1+=u(t1−+I(u(t1, u'(t1+ =u' (t1−+J(u(t1, u(0=u(T, u'(0=u'(T, new criteria are established based on Schaefer's fixed-point theorem.

  16. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

    Science.gov (United States)

    Biala, T A; Jator, S N

    2015-01-01

    In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process. PMID:26543723

  17. Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

    Institute of Scientific and Technical Information of China (English)

    Xiushan Sun; Lixin Huang; Yinghua Liu; Zhangzhi Cen; Keren Wang

    2005-01-01

    Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions.Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

  18. Existence, Uniqueness and Convergence of Simultaneous Distributed-Boundary Optimal Control Problems

    OpenAIRE

    Gariboldi, Claudia M.; Domingo A. Tarzia

    2015-01-01

    We consider a steady-state heat conduction problem $P$ for the Poisson equation with mixed boundary conditions in a bounded multidimensional domain $\\Omega$. We also consider a family of problems $P_{\\alpha}$ for the same Poisson equation with mixed boundary conditions being $\\alpha>0$ the heat transfer coefficient defined on a portion $\\Gamma_{1}$ of the boundary. We formulate simultaneous \\emph{distributed and Neumann boundary} optimal control problems on the internal energy $g$ within $\\Om...

  19. Dynamic programming for infinite horizon boundary control problems of PDE's with age structure

    CERN Document Server

    Faggian, Silvia

    2008-01-01

    We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the associated stationary Hamilton--Jacobi--Bellman equation and use this to prove existence and uniqueness of feedback controls. The idea of studying this kind of problem comes from economic applications, in particular from models of optimal investment with vintage capital. Such family of problems has already been studied in the finite horizon case by Faggian. The infinite horizon case is more difficult to treat and it is more interesting from the point of view of economic applications, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is here performed through a nontrivial limiting procedure from the corresponding finite horizon problem.

  20. Nonresonance conditions for fourth order nonlinear boundary value problems

    OpenAIRE

    F. Munyamarere; C. Fabry; De Coster, C.

    1994-01-01

    This paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2À),   u′(0)=u′(2À),   u″(0)=u″(2À),   u‴(0)=u‴(2À).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. We obtain existence c...

  1. Positive solutions and singular discrete boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Cecchi, M.; Došlá, Zuzana; Marini, M.

    2004-01-01

    Roč. 4, - (2004), s. 271-283. ISSN 1085-3375 Institutional research plan: CEZ:AV0Z1019905 Keywords : second - order nonlinear difference equation * singular nonlinearities * decaying solution Subject RIV: BA - General Mathematics

  2. Preconditioning of boundary value problems using elementwise Schur complements

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Blaheta, Radim; Neytcheva, M.

    2009-01-01

    Roč. 31, č. 2 (2009), s. 767-789. ISSN 0895-4798 Institutional research plan: CEZ:AV0Z30860518 Keywords : preconditioning methods * multilevel methods * two-by-two block partitioning Subject RIV: BA - General Mathematics Impact factor: 2.411, year: 2009 http://dx.doi.org/10.1137/070679673

  3. On numerical-analytic techniques for boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Shchobak, N.

    2012-01-01

    Roč. 12, č. 3 (2012), s. 5-10. ISSN 1335-8243 Institutional support: RVO:67985840 Keywords : numerical-analytic method * periodic successive approximations * Lyapunov-Schmidt method Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/aeei.2012.12.issue-3/v10198-012-0035-1/v10198-012-0035-1.xml?format=INT

  4. RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

    KAUST Repository

    Farrell, Patricio

    2013-01-01

    In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.

  5. Numerical study of one-dimensional Stefan problem with periodic boundary conditions

    OpenAIRE

    Qu Liang-Hui; Ling Feng; Xing Lin

    2013-01-01

    A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

  6. Numerical study of one-dimensional Stefan problem with periodic boundary conditions

    Directory of Open Access Journals (Sweden)

    Qu Liang-Hui

    2013-01-01

    Full Text Available A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

  7. Chlorine-36 and the initial value problem

    Science.gov (United States)

    Davis, Stanley N.; Cecil, DeWayne; Zreda, Marek; Sharma, Pankaj

    Chlorine-36 is a radionuclide with a half-life of 3.01×105a. Most 36Cl in the hydrosphere originates from cosmic radiation interacting with atmospheric gases. Large amounts were also produced by testing thermonuclear devices during 1952-58. Because the monovalent anion, chloride, is the most common form of chlorine found in the hydrosphere and because it is extremely mobile in aqueous systems, analyses of both total Cl- as well as 36Cl have been important in numerous hydrologic studies. In almost all applications of 36Cl, a knowledge of the initial, or pre-anthropogenic, levels of 36Cl is useful, as well as essential in some cases. Standard approaches to the determination of initial values have been to: (a) calculate the theoretical cosmogenic production and fallout, which varies according to latitude; (b) measure 36Cl in present-day precipitation and assume that anthropogenic components can be neglected; (c) assume that shallow groundwater retains a record of the initial concentration; (d) extract 36Cl from vertical depth profiles in desert soils; (e) recover 36Cl from cores of glacial ice; and (f) calculate subsurface production of 36Cl for water that has been isolated from the atmosphere for more than one million years. The initial value from soil profiles and ice cores is taken as the value that occurs directly below the depth of the easily defined bomb peak. All six methods have serious weaknesses. Complicating factors include 36Cl concentrations not related to cosmogenic sources, changes in cosmogenic production with time, mixed sources of chloride in groundwater, melting and refreezing of water in glaciers, and seasonal groundwater recharge that does not contain average year-long concentrations of 36Cl. Résumé Le chlore-36 est un radionucléide de période 3.01×105a. Pour l'essentiel, le 36Cl dans l'hydrosphère provient des effets du rayonnement cosmique sur les gaz atmosphériques. De grandes quantités de 36Cl ont aussi été produites au cours des

  8. Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions

    CERN Document Server

    Latyshev, A V

    2012-01-01

    Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the gaseous molecules is constructed. The velocity of gas in half-space is found, also its value direct at a wall is found. The force resistance operating from gas on border is found. Besides, the capacity of dissipation of the energy falling to unit of area of the fluctuating plate limiting gas is obtained.

  9. Optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian

    CERN Document Server

    Yang, Ray

    2011-01-01

    We discuss the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.

  10. Cost-effective computations with boundary interface operators in elliptic problems

    International Nuclear Information System (INIS)

    The numerical algorithm for fast computations with interface operators associated with the elliptic boundary value problems (BVP) defined on step-type domains is presented. The algorithm is based on the asymptotically almost optimal technique developed for treatment of the discrete Poincare-Steklov (PS) operators associated with the finite-difference Laplacian on rectangles when using the uniform grid with a 'displacement by h/2'. The approach can be regarded as an extension of the method proposed for the partial solution of the finite-difference Laplace equation to the case of displaced grids and mixed boundary conditions. It is shown that the action of the PS operator for the Dirichlet problem and mixed BVP can be computed with expenses of the order of O(Nlog2N) both for arithmetical operations and computer memory needs, where N is the number of unknowns on the rectangle boundary. The single domain algorithm is applied to solving the multidomain elliptic interface problems with piecewise constant coefficients. The numerical experiments presented confirm almost linear growth of the computational costs and memory needs with respect to the dimension of the discrete interface problem. 14 refs., 3 figs., 4 tabs

  11. The boundary element method for the solution of the multidimensional inverse heat conduction problem

    International Nuclear Information System (INIS)

    This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author)

  12. A Flexible Far Field Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

    OpenAIRE

    Nordström, Jan; Abbas, Qaisar; A. Erickson, Brittany; Frenander, Hannes

    2013-01-01

    A new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied at far field boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new ...

  13. A Dynamic Boundary Guarding Problem with Translating Targets

    CERN Document Server

    Smith, Stephen L; Bullo, Francesco

    2009-01-01

    We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, ...

  14. Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method

    Institute of Scientific and Technical Information of China (English)

    KEUM Bangyong; LIU Yijun

    2005-01-01

    The development of two boundary element algorithms for solving 3-D, frictional, and linear elastostatic contact problems is reported in this paper. The algorithms employ nonconforming discretizations for solving 3-D boundary element models, which provide much needed flexibility in the boundary element modeling for 3-D contact problems. These algorithms are implemented in a new 3-D boundary element code and verified using several examples. For the numerical examples studied, the results using the new boundary element algorithms match very well with the results using a commercial finite element code, and clearly demonstrate the feasibility of the new boundary element approach for 3-D contact analysis.

  15. Some moving boundary problems in underground energy processes

    Science.gov (United States)

    Zheng, Zhong

    In this thesis, we study four moving boundary problems motivated by underground energy processes such as enhancing oil recovery and geological CO2 sequestration. The major focus is the time evolution of the fluid-fluid interface under the effect of confinement, heterogeneity, drainage, and unfavorable viscosity ratio. Specifically, in Chapter 2, theoretical and numerical investigations are combined to study the effect of confinement when a fluid is injected into a porous medium saturated with another immiscible fluid. In the early time period, the effect of confinement is negligible, whereas the confinement effect becomes significant in the late time period. The flow behaviour is summarized in a regime diagram with five distinct dynamical regimes that characterize the shape of the interface: a nonlinear diffusion regime, a transition regime, a traveling wave regime, an equal viscosity regime, and a rarefaction wave regime. The thesis continues in Chapter 3 with a theoretical study based on a phase-plane analysis of the effect of horizontal heterogeneity, which eventually reveals the existence of a second-kind self-similar solution when a viscous gravity current is propagating toward the origin. Scaling arguments alone do not work in this case, because there exists a natural length scale, i.e., the distance between the origin and the initial location of the fluid, and hence a natural time scale, i.e., the time for the front to reach the origin. Experimental and numerical results are also provided to support the theoretical predictions. Our study on drainage, described in Chapter 4, provides a self-similar solution to describe the buoyancy-driven fluid drainage process. Previous reports mainly focus on the propagation problem when the information on the global mass is given. In contrast, in a fluid drainage process the time evolution of the global mass is obtained as the solution of the problem. The thesis closes in Chapter 5, with theoretical and experimental

  16. A Computational Study of the Boundary Value Methods and the Block Unification Methods for ${y}^{?}=f(x,y,{y}^{\\prime })$

    OpenAIRE

    Biala, T. A.

    2016-01-01

    We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency.

  17. A coupling procedure for modeling acoustic problems using finite elements and boundary elements

    OpenAIRE

    Coyette, J.; Vanderborck, G.; Steichen, W.

    1994-01-01

    Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...

  18. Effective Boundary Treatment for the Biharmonic Dirichlet Problem

    Science.gov (United States)

    Brandt, A.; Dym, J.

    1996-01-01

    The biharmonic equation can be rewritten as a system of two Poisson equations. Multigrid solution of this system is expected to converge with the same amount of work as solving two Poisson equations, requiring less than 70 floating point operations (scalar multiply or addition) per fine grid point to reach a solution using an FMG algorithm. For periodic boundary conditions, this goal is attained by simple, straightforward application of multigrid. For Dirichlet boundary conditions, however, convergence is impeded by poor interaction with the boundaries. Attempts to overcome the slowness without specifically addressing the boundaries have resulted in multigrid algorithms not attaining the Poisson convergence rate. We present three methods of boundary treatment with which full multigrid efficiency can be obtained. All implement an approach described by Brandt, concentrating some additional effort near the boundary. The first approach simply adds a number of relaxation sweeps over points close to the boundary. The second uses joint relaxation on near-boundary points. The third method takes something from each of the first two methods, resulting in a solver more suitable for highly parallel applications.

  19. Inverse Boundary Problems for Systems in Two Dimensions

    CERN Document Server

    Albin, Pierre; Tzou, Leo; Uhlmann, Gunther

    2011-01-01

    We prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary, and consider both a Dirac-type operator plus potential acting on sections of a Clifford bundle and a connection Laplacian plus potential (i.e. Schr\\"odinger Laplacian with external Yang-Mills field) acting on sections of a Hermitian bundle. In either case we show that the Cauchy data determines both the connection and the potential up to a natural gauge transformation: conjugation by an endomorphism of the bundle which is the identity at the boundary. For domains of $\\mathbb{C}$, we recover zeroth order terms up to gauge from Cauchy data at the boundary in first order elliptic systems.

  20. Boundary values as Hamiltonian variables. II. Graded structures

    Science.gov (United States)

    Soloviev, Vladimir O.

    2002-07-01

    It is shown that the new formula for the field theory Poisson brackets arises naturally in the proposed extension of the formal variational calculus incorporating divergences. The linear spaces of local functionals, evolutionary vector fields, functional forms, multi-vectors and differential operators become graded with respect to divergences. The bilinear operations, such as the action of vector fields onto functionals, the commutator of vector fields, the interior product of forms and vectors and the Schouten-Nijenhuis bracket are compatible with the grading. A definition of the adjoint graded operator is proposed and antisymmetric operators are constructed with the help of boundary terms. The fulfilment of the Jacobi identity for the new Poisson brackets is shown to be equivalent to vanishing of the Schouten-Nijenhuis bracket of the Poisson bivector with itself.

  1. Value-At-Risk Optimal Policies for Revenue Management Problems

    OpenAIRE

    Koenig, M; Meissner, J

    2010-01-01

    Consider a single-leg dynamic revenue management problem with fare classes controlled by capacity in a risk-averse setting. The revenue management strategy aims at limiting the down-side risk, and in particular, value-at-risk. A value-at-risk optimised policy offers an advantage when considering applications which do not allow for a large number of reiterations. They allow for specifying a confidence level regarding undesired scenarios. We state the underlying problem as a Markov decision pro...

  2. LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

    Institute of Scientific and Technical Information of China (English)

    Wang Xiaohua; Yi Fahuai; Yang Zhou

    2005-01-01

    This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary Γ:y = g(x, t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.

  3. Boundary Values for Regional to Continental Scale Greenhouse Gas Flux Estimation

    Science.gov (United States)

    Andrews, A. E.; Basu, S.; Benmergui, J. S.; Dlugokencky, E. J.; Karion, A.; Masarie, K. A.; Michalak, A. M.; Mountain, M. E.; Nehrkorn, T.; Stein, A. F.; Sweeney, C.; Tans, P. P.; Thoning, K. W.; Trudeau, M.; Yadav, V.

    2015-12-01

    Errors in prescribed boundary values can bias estimates of surface fluxes in data-assimilation and inverse modeling studies of regional greenhouse gas budgets. Sensitivity to boundary value errors is particularly important for CO2, since strong seasonally opposing fluxes result in comparatively small net annual uptake. We have developed empirical boundary value products for North America for CO2, CH4, N2O and other long-lived gases using data from aircraft profiles and marine boundary layer sites in NOAA's Global Greenhouse Gas Reference Network. The influence of each aircraft sample is mapped forward and backward from the measurement location using trajectories generated with NOAA's HYSPLIT model driven by meteorological fields from the North American Regional Reanalysis system. These data and influence functions are used to create free-tropospheric reference surfaces that describe monthly scale variability as a function of longitude, latitude, altitude, and time. Data from remote marine boundary layer sites are used to generate Atlantic and Pacific marine boundary layer reference surfaces that vary with latitude, altitude and time. Taken together, the free-troposphere and marine boundary layer reference surfaces provide 4-dimensional boundary values for the continent. This product has been significantly improved compared to earlier versions used in several published studies. We have also developed a related framework for simultaneous optimization of boundary values and surface fluxes in the NOAA CarbonTracker-Lagrange regional inverse modeling system, which uses surface and boundary value footprints from the WRF-STILT model. In this case, we adjust a prior estimate for the boundary values such as can be obtained from the global Eulerian CarbonTracker modeling system or another global model. Vertically resolved data from aircraft and/or from a combination of surface and column measurements are needed to reliably separate surface and boundary influences. We will

  4. The problem of criticality and initial-value problem in neutron transport theory

    International Nuclear Information System (INIS)

    The problem of criticality and the initial value problem are studied in the case of a linear Boltzmann equation and of both finite and infinite media. The space of functions where the problems are solved is chosen in such a way as to cover a wide range of physical situations. The asymptotic time behavior of the solution to the initial-value problem is also discussed, and main results are summarized in three basic theorems. (author)

  5. Picard iterations of boundary-layer equations. [in singular-perturbation analysis of flightpath optimization problems

    Science.gov (United States)

    Ardema, M. D.; Yang, L.

    1985-01-01

    A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.

  6. Vacuum expectation value asymptotics for second order differential operators on manifolds with boundary

    CERN Document Server

    Branson, T P; Vasilevich, D V

    1998-01-01

    Let M be a compact Riemannian manifold with smooth boundary. We study the vacuum expectation value of an operator Q by studying Tr Qe^{-tD}, where D is an operator of Laplace type on M, and where Q is a second order operator with scalar leading symbol; we impose Dirichlet or modified Neumann boundary conditions.

  7. Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

    Institute of Scientific and Technical Information of China (English)

    Kuetche Kamgang Victor; Gambo Betchewe; Bouetou Bouetou Thomas; Timoleon Crepin Kofane

    2009-01-01

    We investigate the dynamical behaviour of a coupled dispersionlees system (CDS) by solving its initial-value problem following a dynamical system approach.As a result,we unearth a typical miscellaneous travelling waves including the localized and periodic ones.We also investigate the energy density of such waves and find that under some boundary conditions,the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most stable travelling waves in another situation of boundary conditions.

  8. Mimetic Discretization of Vector-valued Diffusion Problems

    DEFF Research Database (Denmark)

    Olesen, Kennet

    2016-01-01

    for problems involving gradients of scalar fields and the curl and divergence of vector fields. This is done by expressing the physical quantities using real-valued differential forms. In this work problems involving the gradient of a vector field and the divergence of a second order tensor are...... considered. This implies the use of vector- and covector-valued differential forms. Special considerations are taken to maintain the intrinsic nature of the operators. Several solutions to relevant 2D problems are shown to document the preserving nature of the method and the attractive convergence rates...

  9. Exact Multiplicity of Positive Solutions for a Class of Second-Order Two-Point Boundary Problems with Weight Function

    OpenAIRE

    Luo Hua; An Yulian

    2010-01-01

    An exact multiplicity result of positive solutions for the boundary value problems , , , is achieved, where is a positive parameter. Here the function is and satisfies , for for some . Moreover, is asymptotically linear and can change sign only once. The weight function is and satisfies , for . Using bifurcation techniques, we obtain the exact number of positive solutions of the problem under consideration for lying in various intervals in . Moreover, we indic...

  10. Optimal stability polynomials for numerical integration of initial value problems

    KAUST Repository

    Ketcheson, David I.

    2013-01-08

    We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.

  11. Conforming Discretizations of Boundary Element Solutions of the Electroencephalography Forward Problem

    CERN Document Server

    Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P

    2016-01-01

    In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...

  12. BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

    Institute of Scientific and Technical Information of China (English)

    DONG Zheng-zhu; LI Shun-cai; YU De-hao

    2006-01-01

    After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

  13. Linear second-order problems with Sturm-Liouville-type multi-point boundary conditions

    Directory of Open Access Journals (Sweden)

    Bryan P. Rynne

    2012-08-01

    Full Text Available We consider the eigenvalue problem for the equation $-u'' = lambda u$ on $(-1,1$, together with general Sturm-Liouville-type, multi-point boundary conditions at $pm 1$. We show that the basic spectral properties of this problem are similar to those of the standard Sturm-Liouville problem with separated boundary conditions. In particular, for each integer $k ge 0$ there exists a unique, simple eigenvalue $lambda_k$ whose eigenfunctions have 'oscillation count' equal to k.

  14. Inverse minimum spanning tree problem and reverse shortest-path problem with discrete values

    Institute of Scientific and Technical Information of China (English)

    LIU Longcheng; HE Yong

    2006-01-01

    In this paper, we consider two network improvement problems with given discrete values: the inverse minimum spanning tree problem and the reverse shortest-path problem, where the decrements of the weight of the edges are given discrete values. First,for the three models of the inverse minimum spanning tree problem (the sum-type, the bottleneck-type and the constrained bottlenecktype), we present their respective strongly polynomial algorithms. Then, we show that the reverse shortest-path problem is strongly NP-complete.

  15. A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

    Directory of Open Access Journals (Sweden)

    TIAN Jialei

    2015-11-01

    Full Text Available By using the ground as the boundary, Molodensky problem usually gets the solution in form of series. Higher order terms reflect the correction between a smooth surface and the ground boundary. Application difficulties arise from not only computational complexity and stability maintenance, but also data-intensiveness. Therefore, in this paper, starting from the application of external gravity disturbance, Green formula is used on digital terrain surface. In the case of ignoring the influence of horizontal component of the integral, the expression formula of external disturbance potential determined by boundary value consisted of ground gravity anomalies and height anomaly difference are obtained, whose kernel function is reciprocal of distance and Poisson core respectively. With this method, there is no need of continuation of ground data. And kernel function is concise, and suitable for the stochastic computation of external disturbing gravity field.

  16. Accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior measurements, I. Boundary-value techniques

    CERN Document Server

    Plaster, B

    2013-01-01

    We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar potential will satisfy a Laplace equation. Therefore, if either the vector field components or the normal derivative of the scalar potential can be measured on the surface of this boundary, thus defining a Dirichlet or Neumann boundary-value problem, respectively, the interior vector field components or the scalar potential (and, thus, the field components via the gradient of the potential) can be uniquely determined via solution of the Laplace equation. We discuss the applicability of this technique to the determination of the interior magnetic field components during the operating phase of neutron electric dipole moment experim...

  17. FLUOMEG: a planar finite difference mesh generator for fluid flow problems with parallel boundaries

    International Nuclear Information System (INIS)

    A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables

  18. Semi-Toeplitz preconditioning for linearized boundary layer problems

    OpenAIRE

    Sundberg, Samuel

    2002-01-01

    We have defined and analyzed a semi-Toeplitz preconditioner for time-dependent and steady-state convection-diffusion problems. Analytic expressions for the eigenvalues of the preconditioned systems are obtained. An asymptotic analysis shows that the eigenvalue spectrum of the time-dependent problem is reduced to two eigenvalues when the number of grid points go to infinity. The numerical experiments sustain the results of the theoretical analysis, and the preconditioner exhibits a robust beha...

  19. Investigation of one inverse problem in case of modeling water areas with "liquid" boundaries

    Science.gov (United States)

    Sheloput, Tatiana; Agoshkov, Valery

    2015-04-01

    In hydrodynamics often appears the problem of modeling water areas (oceans, seas, rivers, etc.) with "liquid" boundaries. "Liquid" boundary means set of those parts of boundary where impermeability condition is broken (for example, straits, bays borders, estuaries, interfaces of oceans). Frequently such effects are ignored: for "liquid" boundaries the same conditions are used as for "solid" ones, "material boundary" approximation is applied [1]. Sometimes it is possible to interpolate the results received from models of bigger areas. Moreover, approximate estimates for boundary conditions are often used. However, those approximations are not always valid. Sometimes errors in boundary condition determination could lead to a significant decrease in the accuracy of the simulation results. In this work one way of considering the problem mentioned above is described. According to this way one inverse problem on reconstruction of boundary function in convection-reaction-diffusion equations which describe transfer of heat and salinity is solved. The work is based on theory of adjoint equations [2] and optimal control, as well as on common methodology of investigation inverse problems [3]. The work contains theoretical investigation and the results of computer simulation applied for the Baltic Sea. Moreover, conditions and restrictions that should be satisfied for solvability of the problem are entered and justified in the work. Submitted work could be applied for the solution of more complicated inverse problems and data assimilation problems in the areas with "liquid" boundaries; also it is a step for developing algorithms on computing level, speed, temperature and salinity that could be applied for real objects. References 1. A. E. Gill. Atmosphere-ocean dynamics. // London: Academic Press, 1982. 2. G. I. Marchuk. Adjoint equations. // Moscow: INM RAS, 2000, 175 p. (in Russian). 3. V.I. Agoshkov. The methods of optimal control and adjoint equations in problems of

  20. Stability of basis property of a periodic problem with nonlocal perturbation of boundary conditions

    Science.gov (United States)

    Imanbaev, Nurlan; Sadybekov, Makhmud

    2016-08-01

    The present work is the continuation of authors' researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. In this paper a spectral problem for a multiple differentiation operator with an integral perturbation of boundary conditions of one type, which are regular, but not strongly regular, is devoted. For this type of the boundary conditions it is known that the unperturbed problem has an asymptotically simple spectrum, and its system of normalized eigenfunctions creates the Riesz basis. We construct the characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. It is shown that the Riesz basis property of a system of eigen and adjoint functions is stable with respect to integral perturbations of the boundary condition. In the paper requirements of smoothness to the kernel of the integral perturbation are also reduced (unlike our previous researchers).