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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. Riemann Boundary Value Problems for Koch Curve

    Directory of Open Access Journals (Sweden)

    Zhengshun Ruanand

    2012-11-01

    Full Text Available In this study, when L is substituted for Koch curve, Riemann boundary value problems was defined, but generally speaking, Cauchy-type integral is meaningless on Koch curve. When some analytic conditions are attached to functions G (z and g (z, through the limit function of a sequence of Cauchytype integrals, the homogeneous and non-homogeneous Riemann boundary problems on Koch curve are introduced, some similar results was attained like the classical boundary value problems for analytic functions.

  3. 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

  4. 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.

  5. 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.

  6. 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...

  7. 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.

  8. Separable boundary-value problems in physics

    CERN Document Server

    Willatzen, Morten

    2011-01-01

    Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations i

  9. 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...

  10. Superlinear singular fractional boundary-value problems

    Directory of Open Access Journals (Sweden)

    Imed Bachar

    2016-04-01

    Full Text Available In this article, we study the superlinear fractional boundary-value problem $$\\displaylines{ D^{\\alpha }u(x =u(xg(x,u(x,\\quad 00$. The function $g(x,u\\in C((0,1\\times [ 0,\\infty ,[0,\\infty$ that may be singular at x=0 and x=1 is required to satisfy convenient hypotheses to be stated later.

  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. 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.

  13. 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.

  14. 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...

  15. 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 $T$.

  16. 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.

  17. 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.

  18. 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.

  19. 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...

  20. 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...

  1. 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.

  2. 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.

  3. A boundary value problem for hypermonogenic functions in Clifford analysis

    Institute of Scientific and Technical Information of China (English)

    QIAO; Yuying

    2005-01-01

    This paper deals with a boundary value problem for hypermonogenic functions in Clifford analysis. Firstly we discuss integrals of quasi-Cauchy's type and get the Plemelj formula for hypermonogenic functions in Clifford analysis, and then we address Riemman boundary value problem for hypermonogenic functions.

  4. A Kind of Boundary Value Problem for Hypermonogenic Function Vectors

    Institute of Scientific and Technical Information of China (English)

    He Ju YANG; Yong Hong XIE; Yu Ying QIAO

    2011-01-01

    By the Plemelj formula and the compressed fixed point theorem, this paper discusses a kind of boundary value problem for hypermonogenic function vectors in Clifford analysis. And the paper proves the existence and uniqueness of the solution to the boundary value problem for hypermonogenic function vectors in Clifford analysis.

  5. Pseudo almost periodic solutions to parabolic boundary value inverse problems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    We first define the pseudo almost periodic functions in a more general setting.Then we show the existence,uniqueness and stability of pseudo almost periodic solutions of parabolic inverse problems for a type of boundary value problems.

  6. 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.

  7. POSITIVE SOLUTIONS TO A SEMIPOSITONE SINGULAR NEUMANN BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    A semipositone singular boundary value problem (BVP for short) is discussed in this paper. By Krasnaselskii's fixed point theorem in cones,we derive suffcient conditions,which guarantee that the semipositone BVP has at least one positive solution.

  8. Reconsideration on Homogeneous Quadratic Riemann Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    Lu Jian-ke

    2004-01-01

    The homogeneous quadratic Riemann boundary value problem (1) with Hǒlder continuous coefficients for the normal case was considered by the author in 1997. But the solutions obtained there are incomplete. Here its general method of solution is obtained.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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...

  14. QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In this paper we shall consider a discontinuous nonlinear nonmonotone elliptic boundary value problem, i.e. a quasilinear elliptic hemivariational inequality. This kind of problems is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, we will prove the existence of solutions.

  15. A NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    YANJINHAI

    1996-01-01

    The existenoe and limit hehaviour of the solution for a kind of nonloeal noulinear boundary value condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinks to a point in a certain way, this condition either results in a Dirac measure or simply disappears in the corresponding problem.

  16. 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.

  17. Nonlinear boundary value problem for biregular functions in Clifford analysis

    Institute of Scientific and Technical Information of China (English)

    黄沙

    1996-01-01

    The biregular function in Clifford analysis is discussed. Plemelj’s formula is obtained andnonlinear boundary value problem: is considered. Applying the methodof integral equations and Schauder fixed-point theorem, the existence of solution for the above problem is proved.

  18. RIEMANN BOUNDARY VALUE PROBLEMS WITH GIVEN PRINCIPAL PART

    Institute of Scientific and Technical Information of China (English)

    Li Weifeng; Du Jinyuan

    2009-01-01

    In this article, the authors discuss the Riemann boundary value problems with given principal part. First, authors consider a special case and give a classification of the solution class Rn by the way. And then, they consider the general case. The solvable conditions for this problem and its solutions is obtained when it is solvable.

  19. A numerical solution of a singular boundary value problem arising in boundary layer theory.

    Science.gov (United States)

    Hu, Jiancheng

    2016-01-01

    In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors. PMID:27026894

  20. A Kind of Boundary Element Methods for Boundary Value Problem of Helmholtz Equation

    Institute of Scientific and Technical Information of China (English)

    张然; 姜正义; 马富明

    2004-01-01

    Problems for electromagnetic scattering are of significant importance in many areas of technology. In this paper we discuss the scattering problem of electromagnetic wave incident by using boundary element method associated with splines. The problem is modelled by a boundary value problem for the Helmholtz eouation

  1. 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...

  2. 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.

  3. 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.

  4. INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION

    Institute of Scientific and Technical Information of China (English)

    陈国旺

    2003-01-01

    In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equationare proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.

  5. 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.

  6. Non-Homogeneous Riemann Boundary Value Problem with Radicals

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The solution of the non-homogeneous Riemann boundary value problem with radicals (1.2)together with its condition of solvability is obtained for arbitrary positive integers p and q, which generalizes the results for the case p=q=2.

  7. Boundary value problems with shift for generalized analytic vectors

    Directory of Open Access Journals (Sweden)

    Nino Manjavidze

    2010-03-01

    Full Text Available This paper is a survey of the most important work of the well-known Georgian mathematician Professor Giorgi Manjavidze “Boundary value problems for analytic and generalized analytic functions”. Here we present his original approach to the subject. The main attention is paid to the construction of the canonical matrices which are used in the construction of the general solutions of the considered problems. Explicit conditions of normal solvability and index formulas are obtained.

  8. 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.

  9. 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.

  10. Noncontinuous data boundary value problems for Schr(o)dinger equation in Lipschitz domains

    Institute of Scientific and Technical Information of China (English)

    TAO Xiangxing

    2006-01-01

    The noncontinuous data boundary value problems for Schr(o)dinger equations in Lipschitz domains and its progress are pointed out in this paper.Particularly,the Lp boundary value problems with p>1,and Hp boundary value problems with p<1 have been studied.Some open problems about the Besov-Sobolev and Orlicz boundary value problems are given.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. On Systems of Boundary Value Problems for Differential Inclusions

    Institute of Scientific and Technical Information of China (English)

    Lynn ERBE; Christopher C. TISDELL; Patricia J. Y. WONG

    2007-01-01

    Herein we consider the existence of solutions to second-order,two-point boundary value problems (BVPs) for systems of ordinary differential inclusions.Some new Bernstein –Nagumo condi-tions are presented that ensure a priori on the derivative of solutions to the differential inclusion.These a priori results are then applied,in conjunction with appropriate topological methods,to prove some new existence theorems for solutions to systems of BVPs for differential inclusions.The new conditions allow of the treatment of systems of BVPs without growth restrictions.

  17. Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems

    Directory of Open Access Journals (Sweden)

    A. Boichuk

    2011-01-01

    Full Text Available Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of n ordinary differential equations with constant coefficients and single delay (in the linear part and with a finite number of measurable delays of argument in nonlinearity: ż(t=Az(t-τ+g(t+εZ(z(hi(t,t,ε,  t∈[a,b], assuming that these solutions satisfy the initial and boundary conditions z(s:=ψ(s if s∉[a,b],  lz(⋅=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functional l does not coincide with the number of unknowns in the differential system with a single delay.

  18. Chebyshev Finite Difference Method for Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Boundary

    2015-09-01

    Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

  19. 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.

  20. 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...

  1. THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Mujeeb ur Rehman; Rahmat Ali Khan; Naseer Ahmad Asif

    2011-01-01

    In this paper,we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type cDδ0+u(t) =f(t,u(t),cDσ0+u(t)),t ∈[0,T],u(0) =αu(η),u(T) =βu(η),where1 <δ<2,0<σ< 1,α,β∈R,η∈(0,T),αη(1-β)+(1-α)(T-βη) ≠0 and cDoδ+,cDσ0+ are the Caputo fractional derivatives.We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results.Examples are also included to show the applicability of our results.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

    Institute of Scientific and Technical Information of China (English)

    Gregory A. CHECHKIN; Rustem R. GADYL'SHIN

    2007-01-01

    We consider boundary-value problems with rapidly alternating types of boundary condi- tions. We present the classification of homogenized (limit) problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.

  8. 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.

  9. 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

  10. Contrast structure for singular singularly perturbed boundary value problem

    Institute of Scientific and Technical Information of China (English)

    王爱峰; 倪明康

    2014-01-01

    The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step-type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In this paper,authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order.They first give the well posedness of general discontinuous boundary value problems,reduce the discontinuousboundary value problems to a variation problem,and then find the numerical solutions ofabove problem by the finite element method.Finally authors give some error-estimates of the foregoing numerical solutions.

  16. 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.

  17. A Class of Shock Solutions for the Semilinear Singularly Perturbed Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    王庚

    2004-01-01

    The shock solution for the semilinear singularly perturbed two-point boundary value problem was studied. Under suitable conditions and using the theory of differential inequalities, the existence and asymptotic behavior of the solution for the original boundary value problems are discussed. The uniformly effective asymptotic expansion and estimation of solution u(x,ε) were obtained.

  18. 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.

  19. Solution of the Boundary Value Problems with Boundary Conditions in the Form of Gravitational Curvatures

    Science.gov (United States)

    Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.

    2015-12-01

    Values of scalar, vectorial and second-order tensorial 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 are 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. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. 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, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.

  20. MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Yang Liu; Shen Chunfang

    2009-01-01

    Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green's function of these problems are also given.

  1. 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.

  2. 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.

  3. POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    LiHongyu; SunJingxian

    2005-01-01

    By using topological method, we study a class of boundary value problem for a system of nonlinear ordinary differential equations. Under suitable conditions,we prove the existence of positive solution of the problem.

  4. INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    杨灵娥; 郭柏灵; 徐海祥

    2004-01-01

    Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.

  5. 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.

  6. 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.

  7. 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.

  8. The Boundary Value Problem for Elliptic Equation in the Corner Domain

    CERN Document Server

    Zhidkov, E P

    2000-01-01

    This work is devoted to the studies of the solution behavior of the boundary value problem for a nonlinear elliptic equation in the corner domain. The formulation of the boundary value problem arises in magnitostatics when finding the magnetic field distribution by the method of two scalar potentials in the domain comprising ferromagnetic and vacuum. The problem nonlinearity is stipulated by the dependence of the medium properties (magnetic permeability) on the solution to be found. In connection with that the solution of such a problem has to be found by numerical methods, a question arises about the behavior of the boundary value problem solution around the angular point of the ferromagnetic. This work shows that if the magnetic permeability function meets certain requirments, the corresponding solution of the boundary value problem will have a limited gradient.

  9. A Boundary Value Problem for Hermitian Monogenic Functions

    Directory of Open Access Journals (Sweden)

    Ricardo Abreu Blaya

    2008-02-01

    Full Text Available We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in ℝm, m=2n. Necessary and sufficient conditions for the solvability of this problem are obtained.

  10. Laplace Boundary-Value Problem in Paraboloidal Coordinates

    Science.gov (United States)

    Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan

    2012-01-01

    This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

  11. 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.

  12. The initial boundary value problem for free-evolution formulations of General Relativity

    CERN Document Server

    Hilditch, David

    2016-01-01

    We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate primarily on boundaries that are geometrically determined by the outermost normal observer to spacelike slices of the foliation. We present high-order-derivative boundary conditions for the gauge, constraint violating and gravitational wave degrees of freedom of the formulation. Second order derivative boundary conditions are presented in terms of the conformal variables used in numerical relativity simulations. Using Kreiss-Agranovich-Metivier theory we demonstrate, in the frozen coefficient approximation, that with sufficiently high order derivative boundary conditions the initial boundary value problem can be rendered boundary stable. The precise number of derivatives required depends on the gauge. For a choice of the gauge condition that renders the system strongly hyperbolic...

  13. 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.

  14. EXISTENCE AND ITERATION OF POSITIVE SYMMETRIC SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,we consider the existence of symmetric solutions to a nonlinear second order multi-point boundary value problem,and establish corresponding iterative schemes based on the monotone iterative method.

  15. 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.

  16. EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive solutions are established.

  17. 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.

  18. 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.

  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. MULTIPLE POSITIVE SOLUTIONS TO FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,using the Krasnaselskii's fixed point theory in cones and localization method,under more general conditions,the existence of n positive solutions to a class of fourth-order singular boundary value problems is considered.

  1. ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    SunYan; XuBenlong; SunYongping

    2005-01-01

    By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.

  2. 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.

  3. 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

  4. 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.

  5. INITIAL-BOUNDARY VALUE PROBLEM FOR THE LANDAU-LIFSHITZ SYSTEM WITH APPLIED FIELD

    Institute of Scientific and Technical Information of China (English)

    Guo Boling; Ding Shijin

    2000-01-01

    In this paper, the existence and partial regularity of weak solution to the initial-boundary value problem of Landau-Lifshitz equations with applied fields in a 2D bounded domain are obtained by the penalty method.

  6. 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.

  7. Asymptotic behavior of elliptic boundary-value problems with some small coefficients

    Directory of Open Access Journals (Sweden)

    Senoussi Guesmia

    2008-04-01

    Full Text Available The aim of this paper is to analyze the asymptotic behavior of the solutions to elliptic boundary-value problems where some coefficients become negligible on a cylindrical part of the domain. We show that the dimension of the space can be reduced and find estimates of the rate of convergence. Some applications to elliptic boundary-value problems on domains becoming unbounded are also considered.

  8. Solutions to Boundary Value Problem of Nonlinear Impulsive Differential Equation of Fractional Order*

    Institute of Scientific and Technical Information of China (English)

    SU XIN-WEI

    2011-01-01

    This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects. The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in [B. Ahmad, S. Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Analysis: Hybrid Systems, 3(2009), 251258].

  9. 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.

  10. Initial-boundary value problems for a class of nonlinear thermoelastic plate equations

    Institute of Scientific and Technical Information of China (English)

    Zhang Jian-Wen; Rong Xiao-Liang; Wu Run-Heng

    2009-01-01

    This paper studies initial-boundary value problems for a class of nonlinear thermoelastic plate equations. Under some certain initial data and boundary conditions,it obtains an existence and uniqueness theorem of global weak solutions of the nonlinear thermoelstic plate equations,by means of the Galerkin method. Moreover,it also proves the existence of strong and classical solutions.

  11. 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.

  12. GLOBAL SOLUTIONS TO AN INITIAL BOUNDARY VALUE PROBLEM FOR THE MULLINS EQUATION

    Institute of Scientific and Technical Information of China (English)

    Hans-Dieter Alber; Zhu Peicheng

    2007-01-01

    In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L∞(Ω)-norm, as time tends to infinity.

  13. 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...

  14. 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.

  15. 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.

  16. 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

  17. SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

    Institute of Scientific and Technical Information of China (English)

    Ding Haiyun; Ni Mingkang; Lin Wuzhong; Cao Yang

    2012-01-01

    A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article.Using the boundary layer function method,the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved.Numerical result is presented as an illustration to the theoretical result.

  18. 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.

  19. IMPULSIVE BOUNDARY VALUE PROBLEMS FOR STURM-LIOUVILLE TYPE DIFFERENTIAL INCLUSIONS

    Institute of Scientific and Technical Information of China (English)

    Yicheng LIU; Jun WU; Zhixiang LI

    2007-01-01

    In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer's fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.

  20. Free boundary value problems for a class of generalized diffusion equation

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    The transport behavior of free boundary value problems for a class of generalized diffusion equations was studied. Suitable similarity transformations were used to convert the problems into a class of singular nonlinear two-point boundary value problems and similarity solutions were numerical presented for different representations of heat conduction function, convection function, heat flux function, and power law parameters by utilizing the shooting technique. The results revealed the flux transfer mechanism and the character as well as the effects of parameters on the solutions.

  1. 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.

  2. 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.

  3. An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics

    Directory of Open Access Journals (Sweden)

    A. Barari

    2008-01-01

    Full Text Available Variational iteration method (VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM. The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.

  4. 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.

  5. 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.

  6. 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...

  7. 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...

  8. 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.

  9. Solutions for a Class of Singular Nonlinear Boundary Value Problem Involving Critical Exponent

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper, we consider the existence of multiple solutions for a class of singular nonlinear boundary value problem involving critical exponent in Weighted Sobolev Spaces. The existence of two solutions is established by using the Ekeland Variational Principle. Meanwhile, the uniqueness of positive solution for the same problem is also obtained under different assumptions.

  10. POSITIVE SOLUTION TO A CLASS OF SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper,we investigate the existence and uniqueness of positive solutions to a class of singular fractional boundary value problem.The existence of positive solutions to the problem is based on a fixed point theorem in partially ordered sets.

  11. 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

  12. ON SOLUTION OF A KIND OF RIEMANN BOUNDARY VALUE PROBLEM WITH SQUARE ROOTS

    Institute of Scientific and Technical Information of China (English)

    路见可

    2002-01-01

    Solution of the Riemann boundary value problem with square roots (1.1)for analytic functions proposed in [1] is reconsidered, which was solved under certain assumptions on the branch points appeared. Here, the work is continued without these assumptions and the problem is solved in the general case.

  13. EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER NEUMANN BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    Using the fixed point index in cones, we study the existence of one and two positive solutions to singular second order Neumann boundary value problems under some conditions, which concerns the first eigenvalue of the relevant linear problem. Our results improve and extend some known ones in the previous literature.

  14. On an initial-boundary value problem for the nonlinear Schrödinger equation

    Directory of Open Access Journals (Sweden)

    Herbert Gajewski

    1979-01-01

    Full Text Available We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. Adaptation of a two-point boundary value problem solver to a vector-multiprocessor environment

    Energy Technology Data Exchange (ETDEWEB)

    Wright, S.J. (Mathematics Dept., North Carolina State Univ., Raleigh, NC (US)); Pereyra, V. (Weidlinger Associates, Los Angeles, CA (US))

    1990-05-01

    Systems of linear equations arising from finite-difference discretization of two-point boundary value problems have coefficient matrices that are sparse, with most or all of the nonzeros clustered in blocks near the main diagonal. Some efficiently vectorizable algorithms for factorizing these types of matrices and solving the corresponding linear systems are described. The relative effectiveness of the different algorithms varies according to the distribution of initial, final, and coupled end conditions. The techniques described can be extended to handle linear systems arising from other methods for two-point boundary value problems, such as multiple shooting and collocation. An application to seismic ray tracing is discussed.

  1. Existence of Single and Multiple Solutions for First Order Periodic Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    Xiao-ning Lin; Hong Wang; Da-qing Jiang

    2007-01-01

    This paper is devoted to the study of the existence of single and multiple positive solutions for the first order boundary value problem X′=f(t,x),x(0)=x(T),where f∈C([O,T]×R).In addition,we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in the literatures.

  2. 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.

  3. Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method

    Directory of Open Access Journals (Sweden)

    Mustafa Inc

    2014-01-01

    Full Text Available We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM, homotopy perturbation method (HPM, Adomian decomposition method (ADM, variation of parameters method (VPM, and homotopy analysis method (HAM. Obtained results show that our method is very effective.

  4. SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

    Institute of Scientific and Technical Information of China (English)

    Wen Guochun

    2007-01-01

    The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above problem is proved. In this article, the complex analytic method is used, namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed, afterwards the above problem for the degenerate elliptic equations of second order is solved.

  5. Boundary Value Technique for Initial Value Problems Based on Adams-Type Second Derivative Methods

    Science.gov (United States)

    Jator, S. N.; Sahi, R. K.

    2010-01-01

    In this article, we propose a family of second derivative Adams-type methods (SDAMs) of order up to 2k + 2 ("k" is the step number) for initial value problems. The methods are constructed through a continuous approximation of the SDAM which is obtained by multistep collocation. The continuous approximation is used to obtain initial value methods,…

  6. 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...

  7. POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

    Institute of Scientific and Technical Information of China (English)

    Shanying Zhu

    2009-01-01

    This paper deals with the existence of positive solutions to the singular second-order periodic boundary value problem, We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. The Graviton in the AdS-CFT correspondence Solution via the Dirichlet Boundary value problem

    CERN Document Server

    Mück, W

    1998-01-01

    Using the AdS-CFT correspondence we calculate the two point function of CFT energy momentum tensors. The AdS gravitons are considered by explicitly solving the Dirichlet boundary value problem for $x_0=\\epsilon$. We consider this treatment as complementary to existing work, with which we make contact.

  13. 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 .

  14. Positive Solution of Singular Boundary Value Problems on a Half-Line

    Institute of Scientific and Technical Information of China (English)

    Zhong-li Wei; Shao-zhu Chen

    2005-01-01

    This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth solutions on [0, ∞) are given by constructing new lower and upper solutions.

  15. EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.

  16. Existence of Multiple Positive Solutions for Singular Impulsive Boundary Value Problems in Banach Space

    Institute of Scientific and Technical Information of China (English)

    徐西安

    2004-01-01

    In this paper, we first obtain some New results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.

  17. Multiple positive solutions for singular multi-point boundary-value problems with a positive parameter

    Directory of Open Access Journals (Sweden)

    Chan-Gyun Kim

    2014-02-01

    Full Text Available In this article we study the existence, nonexistence, and multiplicity of positive solutions for a singular multi-point boundary value problem with positive parameter. We use the fixed point index theory on a cone and a well-known theorem for the existence of a global continuum of solutions to establish our results.

  18. 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.

  19. 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.

  20. Symmetric solutions of singular nonlocal boundary value problems for systems of differential equation

    Institute of Scientific and Technical Information of China (English)

    KANG Ping; YAO Jianli

    2009-01-01

    In this paper, we investigate the existence of symmetric solutions of singular nonlocal boundary value problems for systems of differential equations. Our analysis relies on a nonlinear alternative of Leray - schauder type. Our results presented here unify, generalize and significantly improve many known results in the literature.

  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. NONTRIVIAL SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.

  3. THREE-POINT BOUNDARY VALUE PROBLEM FOR p-LAPLACIAN DIFFERENTIAL EQUATION AT RESONANCE

    Institute of Scientific and Technical Information of China (English)

    Minggang Zong; Wenyi Cai

    2009-01-01

    By topological degree theory, the three-point boundary value problem for p-Laplacian differential equation at resonance is studied. Some new results on the existence of so-lutions are obtained, which improve and extend some known ones in the previous literatures.

  4. 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.

  5. 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.

  6. 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.

  7. OpenMP for 3D potential boundary value problems solved by PIES

    Science.gov (United States)

    KuŻelewski, Andrzej; Zieniuk, Eugeniusz

    2016-06-01

    The main purpose of this paper is examination of an application of modern parallel computing technique OpenMP to speed up the calculation in the numerical solution of parametric integral equations systems (PIES). The authors noticed, that solving more complex boundary problems by PIES sometimes requires large computing time. This paper presents the use of OpenMP and fast C++ linear algebra library Armadillo for boundary value problems modelled by 3D Laplace's equation and solved using PIES. The testing example shows that the use of mentioned technologies significantly increases speed of calculations in PIES.

  8. MULTIPLE POSITIVE SOLUTIONS TO A SINGULAR THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    In this paper,we study a singular third-order three-point boundary value problem. By a fixed point theorem of cone expansion-compression type due to Krasnosel'skii,we obtain various new results on the existence of two positive solutions to the problem,whose coefficient is allowed to have suitable singularities. Finally,we give an example to verify our results.

  9. 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.

  10. 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.

  11. 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.

  12. Analytic decomposition and numerical procedure for solving the singular boundary value problem arising in viscous flows

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.

  13. 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

  14. The characteristic mixed finite element method and analysis for three-dimensional moving boundary value problem

    Institute of Scientific and Technical Information of China (English)

    袁益让

    1996-01-01

    The software for oil-gas transport and accumulation 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. This thesis, from actual conditions such as the effects of gravitation, buoyancy and capillary pressure, puts forward for the two class boundary value problem a kind of characteristic mixed finite element scheme by making use of the change of region, time step modified techniques of handling boundary value condition, negative norm estimate and the theory of prior estimates. Optimal order estimates in L2 norm are derived for the error in approximate solutions. Thus the well-known theoretical problem proposed by J. Douglas, Jr has been thoroughly and completely solved.

  15. 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.

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

    Science.gov (United States)

    Mustonen, Lauri

    2016-10-01

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

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

    Science.gov (United States)

    Khairullin, Ermek

    2016-08-01

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

  18. Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: An eigenvalue analysis

    Science.gov (United States)

    Warming, Robert F.; Beam, Richard M.

    1986-01-01

    A hyperbolic initial-boundary-value problem can be approximated by a system of ordinary differential equations (ODEs) by replacing the spatial derivatives by finite-difference approximations. The resulting system of ODEs is called a semidiscrete approximation. A complication is the fact that more boundary conditions are required for the spatially discrete approximation than are specified for the partial differential equation. Consequently, additional numerical boundary conditions are required and improper treatment of these additional conditions can lead to instability. For a linear initial-boundary-value problem (IBVP) with homogeneous analytical boundary conditions, the semidiscrete approximation results in a system of ODEs of the form du/dt = Au whose solution can be written as u(t) = exp(At)u(O). Lax-Richtmyer stability requires that the matrix norm of exp(At) be uniformly bounded for O less than or = t less than or = T independent of the spatial mesh size. Although the classical Lax-Richtmyer stability definition involves a conventional vector norm, there is no known algebraic test for the uniform boundedness of the matrix norm of exp(At) for hyperbolic IBVPs. An alternative but more complicated stability definition is used in the theory developed by Gustafsson, Kreiss, and Sundstrom (GKS). The two methods are compared.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Positive solutions for singular three-point boundary-value problems

    Directory of Open Access Journals (Sweden)

    Baoqiang Yan

    2008-08-01

    Full Text Available Using the theory of fixed point index, this paper discusses the existence of at least one positive solution and the existence of multiple positive solutions for the singular three-point boundary value problem: $$displaylines{ y''(t+a(tf(t,y(t,y'(t=0,quad 0

  4. Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Habib Mâagli

    2014-01-01

    fractional boundary value problem:Dαu(x=−a(xuσ(x, x∈(0,1 with the conditions limx→0+⁡x2−αu(x=0, u(1=0, where 1<α≤2, σ∈(−1,1, and a is a nonnegative continuous function on (0,1 that may be singular at x=0 or x=1. We also give the global behavior of such a solution.

  5. MULTIPLE POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH DERIVATIVE DEPENDENCE

    Institute of Scientific and Technical Information of China (English)

    Yan Baoqiang

    2008-01-01

    The existence of at least two positive solutions is presented for the singular second-order boundary value problem {1/p(t)x'(t)'+Φ(t)f(t,x(t),p(t)x'(t)))=0,0<1<1, lim t→0p(t)x'(t) = 0, x(1) = 0, by using the fixed point index, where f may be singular at x = 0 and px' = 0.

  6. 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.

  7. 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

  8. 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...

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

    Science.gov (United States)

    Zhu, Changjiang; Duan, Renjun

    2003-02-01

    This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation \\left\\{\\begin{array}{@{}l@{\\qquad}l@{}} u_t+\\big(\\frac{u^2}{2}\\big)_x=0 x\\gt0\\quad t\\gt0\\\\ u(x,0)=u_0(x) x\\geq0\\\\ u(0,t)=0 t\\geq0. \\end{array}\\right. 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. 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.

  11. Variational solution about over-determined geodetic boundary value problem and its related theories

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.

  12. Variational solution about over-determined geodetic boundary value problem and its related theories

    Institute of Scientific and Technical Information of China (English)

    YU JinHai; PENG FuQing

    2007-01-01

    A new solving method for Laplace equation with over-determined geodetic boundary conditions is proposed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational resulta show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements.

  13. 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 $[t_2, t_3] cap mathbb{T}$.

  14. Analyticity of solutions of analytic non-linear general elliptic boundary value problems,and some results about linear problems

    Institute of Scientific and Technical Information of China (English)

    WANG Rouhuai

    2006-01-01

    The main aim of this paper is to discuss the problem concerning the analyticity of the solutions of analytic non-linear elliptic boundary value problems.It is proved that if the corresponding first variation is regular in Lopatinski(i) sense,then the solution is analytic up to the boundary.The method of proof really covers the case that the corresponding first variation is regularly elliptic in the sense of Douglis-Nirenberg-Volevich,and hence completely generalize the previous result of C.B.Morrey.The author also discusses linear elliptic boundary value problems for systems of ellip tic partial differential equations where the boundary operators are allowed to have singular integral operators as their coefficients.Combining the standard Fourier transform technique with analytic continuation argument,the author constructs the Poisson and Green's kernel matrices related to the problems discussed and hence obtain some representation formulae to the solutions.Some a priori estimates of Schauder type and Lp type are obtained.

  15. 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.

  16. 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.

  17. The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    WANG Jie

    2012-01-01

    We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem Dα0+u(x)=f(x,u(x)), 0<x<1, 3<α≤4u(0) =α0, u″(0) =α2 (1)u(1) =β0, u″(1) =β2where Dα0+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1] x R → R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.

  18. 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.

  19. 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.

  20. PERIODIC BOUNDARY VALUE PROBLEM OF QUASILINEAR SYSTEM%拟线性系统周期边值问题

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    The existence and uniqueness results about quasilinear periodic boundary value problems are established by using the global inverse function theorem and the result about the existence and uniquencess of periodic solutions for the periodic boundary value problem of nonhomogeneous linear periodic system.

  1. A (k, n-k) Conjugate Boundary Value Problem with Semip ositone Nonlinearity

    Institute of Scientific and Technical Information of China (English)

    Yao Qing-liu; Shi Shao-yun

    2015-01-01

    The existence of positive solution is proved for a (k, n−k) conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. (Agarwal R P, Grace S R, O’Regan D. Semipositive higher-order differential equa-tions. Appl. Math. Letters, 2004, 14: 201–207) are extended. The basic tools are the Hammerstein integral equation and the Krasnosel’skii’s cone expansion-compression technique.

  2. The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem

    Science.gov (United States)

    Golse, François; Salvarani, Francesco

    2007-04-01

    Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases, (see Carleman 1957 Problèmes Mathématiques Dans la Théorie Cinétique des Gaz (Uppsala: Almqvist-Wiksells)), set in some bounded interval with boundary conditions prescribing the density of particles entering the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is established for this problem. In fact, the techniques presented here allow treatment generalizations of the Carleman system where the collision frequency is proportional to the αth power of the macroscopic density, with α ∈ [-1, 1].

  3. 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.

  4. Mixed Initial-Boundary Value Problem for the Capillary Wave Equation

    Directory of Open Access Journals (Sweden)

    B. Juarez Campos

    2016-01-01

    Full Text Available We study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u,  t>0,  x>0;  u(x,0=u0(x,  x>0; u(0,t+βux(0,t=h(t,  t>0, where ∂x3/2u=(1/2π∫0∞sign⁡x-y/x-yuyy(y dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Boundary Value Problems for Singular Second-Order Functional Differential Equations

    Institute of Scientific and Technical Information of China (English)

    Hui-zhao Liu; Da-qing Jiang; Yan Wang

    2002-01-01

    Positive solutions to the boundary value problem,{y"=-f(x,y(w(x))),0〈x〈1,αy(x)-βy′(x)=ξ(x),a≤x≤0,γy(x)+δy′(x)=η(x),1≤x≤b, are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0,1] and f(x,y) is a function defined on (0,1)× (0,∞), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong[1].

  11. Fixed set theorems for discrete dynamics and nonlinear boundary-value problems

    Directory of Open Access Journals (Sweden)

    Robert Brooks

    2011-05-01

    Full Text Available We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations

  12. 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.

  13. FREE BOUNDARY VALUE PROBLEM OF ONE DIMENSIONAL TWO-PHASE LIQUID-GAS MODEL

    Institute of Scientific and Technical Information of China (English)

    Wang Zhen; Zhang Hui

    2012-01-01

    n this paper,we study a free boundary value problem for two-phase liquidgas model with mass-depcndent viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously.The gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid.We give the proof of the global existence and uniqueness of weak solutions when β ∈ (0,1),which have improved the result of Evje and Karlsen,and we obtain the regularity of the solutions by energy method.

  14. 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.

  15. 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)

  16. 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.

  17. 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.

  18. Renormalization-group symmetries for solutions of nonlinear boundary value problems

    CERN Document Server

    Kovalev, V F

    2008-01-01

    Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...

  19. 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.

  20. Homotopy deform method for reproducing kernel space for nonlinear boundary value problems

    Indian Academy of Sciences (India)

    MIN-QIANG XU; YING-ZHEN LIN

    2016-10-01

    In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.

  1. 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).

  2. 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.

  3. 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.)

  4. The Initial Boundary Value Problem for the Boltzmann Equation with Soft Potential

    Science.gov (United States)

    Liu, Shuangqian; Yang, Xiongfeng

    2016-08-01

    Boundary effects are central to the dynamics of the dilute particles governed by the Boltzmann equation. In this paper, we study both the diffuse reflection and the specular reflection boundary value problems for the Boltzmann equation with a soft potential, in which the collision kernel is ruled by the inverse power law. For the diffuse reflection boundary condition, based on an L 2 argument and its interplay with intricate {L^∞} analysis for the linearized Boltzmann equation, we first establish the global existence and then obtain the exponential decay in {L^∞} space for the nonlinear Boltzmann equation in general classes of bounded domain. It turns out that the zero lower bound of the collision frequency and the singularity of the collision kernel lead to some new difficulties for achieving the a priori {L^∞} estimates and time decay rates of the solution. In the course of the proof, we capture some new properties of the probability integrals along the stochastic cycles and improve the {L^2-L^∞} theory to give a more direct approach to overcome those difficulties. As to the specular reflection condition, our key contribution is to develop a new time-velocity weighted {L^∞} theory so that we could deal with the greater difficulties stemming from the complicated velocity relations among the specular cycles and the zero lower bound of the collision frequency. From this new point, we are also able to prove that the solutions of the linearized Boltzmann equation tend to equilibrium exponentially in {L^∞} space with the aid of the L 2 theory and a bootstrap argument. These methods, in the latter case, can be applied to the Boltzmann equation with soft potential for all other types of boundary condition.

  5. 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'

  6. 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...

  7. 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.

  8. 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.

  9. 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.

  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. 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 ...

  12. 奇摄动非线性边值问题%THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2000-01-01

    The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities.

  13. 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.

  14. On a difference scheme for nonlocal heat transfer boundary-value problem

    Science.gov (United States)

    Akhymbek, Meiram E.; Sadybekov, Makhmud A.

    2016-08-01

    In this paper, we propose a new method of solving nonlocal problems for the heat equation with finite difference method. The main important feature of these problems is their non-self-adjointness. This non-self-adjointness causes major difficulties in their analytical and numerical solving. The problems, which boundary conditions do not possess strong regularity, are less studied. The scope of study of the paper justifies possibility of building a stable difference scheme with weights for abovementioned type of problems.

  15. 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.

  16. 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.

  17. Investigation of Boundary-Value Problems for the Equation of High Order with Small Parameter at a Higher Derivative

    CERN Document Server

    Amirkhanov, I V; Sarker, N R; Sarhadov, I

    2004-01-01

    In this work the solutions of different boundary-value problems are retrieved analytically and numerically for the equation of high order with small parameter at a higher derivative. The analysis of these solutions is given. It is found that for some variants of symmetric boundary conditions the solutions of a boundary-value problem for the equations of the 4th, 6th, $\\ldots$ orders transfer into the solution of a Schrödinger equation at $\\varepsilon \\to 0$ ($\\varepsilon $ is small parameter). The retrieved solutions with different knots are orthogonal among themselves. The results of numerical calculations are given.

  18. 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.

  19. 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]...

  20. 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.

  1. 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.

  2. 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 r...

  3. 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.

  4. 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.

  5. Acceleration of multiple solution of a boundary value problem involving a linear algebraic system

    Science.gov (United States)

    Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.

    2016-06-01

    Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.

  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. Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    Svatoslav STAN(E)K

    2006-01-01

    The paper presents the conditions which guarantee that for some positive value of μ there are positive solutions of the differential equation (φ(x'))' +μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0, ∞) × (R \\ {0}) of the semipositone type and Q is singular at the value zero of its phase variables.

  8. 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.

  9. 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.

  10. 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.

  11. Existence of solutions of nonlinear two-point boundary value problems for 4nth-order nonlinear differential equation

    Institute of Scientific and Technical Information of China (English)

    高永馨

    2002-01-01

    Studies the existence of solutions of nonlinear two point boundary value problems for nonlinear 4n-th-order differential equation y(4n)= f( t,y,y' ,y",… ,y(4n-1) ) (a) with the boundary conditions g2i(y(2i) (a) ,y(2i+1) (a)) = 0,h2i(y(2i) (c) ,y(2i+1) (c)) = 0, (I= 0,1,…,2n - 1 ) (b) where the functions f, gi and hi are continuous with certain monotone properties. For the boundary value problems of nonlinear nth order differential equation y(n) = f(t,y,y',y",… ,y(n-1)) many results have been given at the present time. But the existence of solutions of boundary value problem (a), (b) studied in this paper has not been covered by the above researches. Moreover, the corollary of the important theorem in this paper, I.e. Existence of solutions of the boundary value problem. Y(4n) = f(t,y,y',y",… ,y(4n-1) ) a2iy(2i) (at) + a2i+1y(2i+1) (a) = b2i ,c2iy(2O ( c ) + c2i+1y(2i+1) ( c ) = d2i, ( I = 0,1 ,…2n - 1) has not been dealt with in previous works.

  12. 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.

  13. On second order periodic boundary-value problems with upper and lower solutions in the reversed order

    Directory of Open Access Journals (Sweden)

    Haiyin Gao

    2006-02-01

    Full Text Available In this paper, we study the differential equation with the periodic boundary value $$displaylines{ u''(t=f(t, u(t, u'(t,quad tin [0, 2pi]cr u(0=u(2pi, quad u'(0=u'(2pi. }$$ The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.

  14. LIFE-SPAN OF CLASSICAL SOLUTIONS OF INITIAL-BOUNDARY VALUE PROBLEM FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS

    Institute of Scientific and Technical Information of China (English)

    Lu Hong

    2007-01-01

    In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in a half-unbounded domain {(t, x)| t ≥ 0, x≥ 0}. Under the assumption that the positive eigenvalues are not all weakly linearly degenerate,we obtain the blow-up phenomenon of the first order derivatives of C1 solution with small and decaying initial data. We also give precise estimate of the life-span of C1 solution.

  15. POSITIVE SOLUTIONS TO A SINGULAR nTH ORDER THREE-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper, we consider a singular nth order three-point boundary value problem with sign changing nonlinearity. By the method of lower solution and topology degree theorem, we investigate the existence of positive solutions to the above problem. Moreover, the associated Green’s function for the above problem is also given. The results of this paper are new and extend the previous known results.

  16. 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.

  17. 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.

  18. A NONLINEAR TRANSFORMATION AND A BOUNDARY-INITIAL VALUE PROBLEM FOR ACLASS OF NONLINEAR CONVECTION-DIFFUSION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    With the aid of a nonlinear transformation, a class of nonlinear convectiondiffusion PDE in one space dimension is converted into a linear one, the unique solution of a nonlinear boundary-initial value problem for the nonlinear PDE can be exactly expressed by the nonlinear transformation, and several illustrative examples are given

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. Sufficient conditions for functions to form Riesz bases in L_2 and applications to nonlinear boundary-value problems

    OpenAIRE

    Peter E. Zhidkov

    2001-01-01

    We find sufficient conditions for systems of functions to be Riesz bases in $L_2(0,1)$. Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz basis in $L_2(0,1)$. The proofs in this article use Bari's theorem.

  4. 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.

  5. MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.

  6. POSITIVE SOLUTIONS TO A CLASS OF SECOND-ORDER SINGULAR SEMIPOSITIVE NEUMANN BOUNDARY VALUE PROBLEM WITH GENERAL FORM

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.

  7. A posteriori estimates for errors of functionals on finite volume approximations to solutions of elliptic boundary value problems

    CERN Document Server

    Angermann, Lutz

    2012-01-01

    This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind discretizations. It is shown how different sources of errors, in particular modeling errors and discretization errors, can be estimated with respect to a user-defined output functional.

  8. SUCCESSIVELY ITERATIVE TECHNIQUE OF SIGN-CHANGING SOLUTION TO A NONLINEAR THIRD-ORDER BOUNDARY VALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    The iterative technique of sign-changing solution is studied for a nonlinear third-order two-point boundary value problem, where the nonlinear term has the time sin-gularity. By applying the monotonically iterative technique, an existence theorem is established and two useful iterative schemes are obtained.

  9. The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    Qing-liu Yao

    2003-01-01

    The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. The Optimal Homotopy Asymptotic Method for the Solution of Higher-Order Boundary Value Problems in Finite Domains

    Directory of Open Access Journals (Sweden)

    Javed Ali

    2012-01-01

    Full Text Available We solve some higher-order boundary value problems by the optimal homotopy asymptotic method (OHAM. The proposed method is capable to handle a wide variety of linear and nonlinear problems effectively. The numerical results given by OHAM are compared with the exact solutions and the solutions obtained by Adomian decomposition (ADM, variational iteration (VIM, homotopy perturbation (HPM, and variational iteration decomposition method (VIDM. The results show that the proposed method is more effective and reliable.

  15. 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.

  16. General Boundary-Value Problems for the Heat Conduction Equation with Piecewise-Continuous Coefficients

    Science.gov (United States)

    Tatsii, R. M.; Pazen, O. Yu.

    2016-03-01

    A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.

  17. Numerical solution of the moving boundary-value problem based on the model of piston-like oil displacement

    Science.gov (United States)

    Astafev, Vladimir; Kasatkin, Andrey

    2016-06-01

    Prediction of the motion of the oil-water contact boundary has great importance in the problems of design of oilfield development by flooding. In this paper we consider a piston-like model of oil-water displacement, which takes into account differences in viscosity and density of the two fluids. Oil reservoir assumed to be homogeneous and infinite, fixed thickness, with constant values of porosity and permeability coefficients. Filtration of liquids is described by Darcy's law. It is assumed, that both fluids are weakly compressible and the pressure in the reservoir satisfies the quasi-stationary diffusion equation. Piston-like displacement model leads to the discontinuity of the tangential component of the velocity vector at the boundary of oil-water contact. Use the Cauchy integral reduces the problem of finding the current boundaries of oil-water contact to the system of singular integral equations for the tangential and normal components of the velocity vector and the Cauchy problem for the integration of the differential equations of motion of the boundary of oil-water contact. An algorithm for the numerical solution of this problem is developed. The monitoring of oil-water boundary motion for different regular and irregular schemes of flooding is carried out.

  18. 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.

  19. Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form

    Directory of Open Access Journals (Sweden)

    Cristian Enache

    2006-06-01

    Full Text Available For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of u(x and |∇u|2, where u(x are the solutions of our problems. From these inequalities, we derive, using Hopf's maximum principles, some maximum principles for the appropriate combinations of u(x and |∇u|2, and we list a few examples of problems to which these maximum principles may be applied.

  20. 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.

  1. Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

    Directory of Open Access Journals (Sweden)

    Zulqurnain Sabir

    2014-06-01

    Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

  2. Upper and lower solutions for a second-order three-point singular boundary-value problem

    Directory of Open Access Journals (Sweden)

    Qiumei Zhang

    2009-09-01

    Full Text Available We study the singular boundary-value problem $$displaylines{ u''+ q(tg(t,u=0,quad t in (0,1,; eta in (0,1,;gamma >0cr u(0=0, quad u(1=gamma u(eta,. }$$ The singularity may appear at $ t=0$ and the function $g$ may be superlinear at infinity and may change sign. The existence of solutions is obtained via an upper and lower solutions method.

  3. Sufficient conditions for functions to form Riesz bases in L_2 and applications to nonlinear boundary-value problems

    Directory of Open Access Journals (Sweden)

    Peter E. Zhidkov

    2001-12-01

    Full Text Available We find sufficient conditions for systems of functions to be Riesz bases in $L_2(0,1$. Then we improve a theorem presented in [13] by showing that a ``standard'' system of solutions of a nonlinear boundary-value problem, normalized to 1, is a Riesz basis in $L_2(0,1$. The proofs in this article use Bari's theorem.

  4. 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

  5. Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Zhang Xuemei

    2009-01-01

    Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of as well as positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

  6. 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...

  7. 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.

  8. 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.

  9. Application of Two-Parameter Extrapolation for Solution of Boundary-Value Problem on Semi-Axis

    CERN Document Server

    Zhidkov, E P

    2000-01-01

    A method for refining approximate eigenvalues and eigenfunctions for a boundary-value problem on a half-axis is suggested. To solve the problem numerically, one has to solve a problem on a finite segment [0,R] instead of the original problem on the interval [0,\\infty). This replacement leads to eigenvalues' and eigenfunctions' errors. To choose R beforehand for obtaining their required accuracy is often impossible. Thus, one has to resolve the problem on [0,R] with larger R. If there are two eigenvalues or two eigenfunctions that correspond to different segments, the suggested method allows one to improve the accuracy of the eigenvalue and the eigenfunction for the original problem by means of extrapolation along the segment. This approach is similar to Richardson's method. Moreover, a two-parameter extrapolation is described. It is combination of the extrapolation along the segment and Richardson's extrapolation along a discretization step.

  10. 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

  11. 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.

  12. Koch曲线上的齐次Riemann边值问题%Homogeneous Riemann Boundary Value Problems for Koch Curve

    Institute of Scientific and Technical Information of China (English)

    阮正顺; 罗艾花

    2012-01-01

    当L为典型的分形曲线-Koch曲线时,提出了Riemann边值问题,但在一般情况下,在Koch曲线上所做的Cauchy型积分无意义.当对已知函数G(z),g(z)增加一定的解析条件,同时利用一列Cauchy型积分的极限函数,对定义在Koch曲线上的齐次Riemann边值问题进行了讨论,并得到与经典解析函数边值问题相类似的结果.%In this paper, when Lis substituted for Koch curve, Riemann boundary value problems was defined, but generally speaking, Cauchy-type integral is meaningless on Koch curve. When some analytic conditions are attached to functions G(z)and g(z), through the limit function of a sequence of Cauchy-type integrals, the homogeneous Riemann boundary problems on Koch curve are introduced, some similar results was attained with the classical boundary value problems for analytic functions.

  13. 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.

  14. 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].

  15. 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.

  16. 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.

  17. Existence and Nonexistence of Positive Solutions for Coupled Riemann-Liouville Fractional Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Johnny Henderson

    2016-01-01

    Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.

  18. 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.

  19. 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.

  20. On the roles of minimization and linearization in least-squares finite element models of nonlinear boundary-value problems

    Science.gov (United States)

    Payette, G. S.; Reddy, J. N.

    2011-05-01

    In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.

  1. 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.

  2. 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.

  3. 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.

  4. Global Weak Solutions of Initial Boundary Value Problem for Boltzmann-Poisson System with Absorbing Boundary%具吸收边界的Bolzmann-Poisson方程组初边值问题的整体弱解

    Institute of Scientific and Technical Information of China (English)

    崔国忠; 张志平; 江成顺

    2002-01-01

    This paper deals with the initial boundary value problem for the BoltzmannPoisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.

  5. 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.

  6. 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...

  7. Extended cubic B-spline method for solving a linear system of second-order boundary value problems.

    Science.gov (United States)

    Heilat, Ahmed Salem; Hamid, Nur Nadiah Abd; Ismail, Ahmad Izani Md

    2016-01-01

    A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The examples suggest that this method produces comparable or more accurate results than cubic B-spline and some other methods.

  8. Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

    Directory of Open Access Journals (Sweden)

    Meiqiang Feng

    2009-01-01

    Full Text Available By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence of Cld[0,1]𝕋 as well as CldΔ[0,1]𝕋 positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.

  9. THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN Ls-SPACES

    Institute of Scientific and Technical Information of China (English)

    WEI Li; ZHOU Haiyun

    2005-01-01

    By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ Ls (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where2 ≤ s < +∞, and 2N/N+1 < p ≤ 2 for N(≥ 1) which denotes the dimension of RN. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.

  10. 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.

  11. 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.

  12. Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations

    Directory of Open Access Journals (Sweden)

    Zdeněk Šmarda

    2009-01-01

    Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.

  13. 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.

  14. 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.

  15. 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.

  16. Accurate numerical resolution of transients in initial-boundary value problems for the heat equation

    CERN Document Server

    Flyer, N

    2003-01-01

    If the initial and boundary data for a PDE do not obey an infinite set of compatibility conditions, singularities will arise in the solution at the corners of the initial time-space domain. For dissipative equations, such as the 1-D heat equation or 1-D convection-diffusion equations, the impacts of these singularities are short lived. However, they can cause a very severe loss of numerical accuracy if we are interested in transient solutions. The phenomenon has been described earlier from a theoretical standpoint. Here, we illustrate it graphically and present a simple remedy which, with only little extra cost and effort, restores full numerical accuracy.

  17. 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.

  18. 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 $u=0$.

  19. 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.

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

    Directory of Open Access Journals (Sweden)

    Said Mesloub

    2008-03-01

    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.

  1. Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution

    Science.gov (United States)

    Belkina, T. A.; Konyukhova, N. B.; Kurochkin, S. V.

    2012-10-01

    A singular boundary value problem for a second-order linear integrodifferential equation with Volterra and non-Volterra integral operators is formulated and analyzed. The equation is defined on ℝ+, has a weak singularity at zero and a strong singularity at infinity, and depends on several positive parameters. Under natural constraints on the coefficients of the equation, existence and uniqueness theorems for this problem with given limit boundary conditions at singular points are proved, asymptotic representations of the solution are given, and an algorithm for its numerical determination is described. Numerical computations are performed and their interpretation is given. The problem arises in the study of the survival probability of an insurance company over infinite time (as a function of its initial surplus) in a dynamic insurance model that is a modification of the classical Cramer-Lundberg model with a stochastic process rate of premium under a certain investment strategy in the financial market. A comparative analysis of the results with those produced by the model with deterministic premiums is given.

  2. An effective numerical method to solve a class of nonlinear singular boundary value problems using improved differential transform method.

    Science.gov (United States)

    Xie, Lie-Jun; Zhou, Cai-Lian; Xu, Song

    2016-01-01

    In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. PMID:27462514

  3. Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions

    Institute of Scientific and Technical Information of China (English)

    Yi-cheng Liu; Jun Wu; Zhi-xiang Li

    2007-01-01

    In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.

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

    Directory of Open Access Journals (Sweden)

    Doria Celso Melchiades

    2005-01-01

    Full Text Available It is shown that the nonhomogeneous Dirichlet and Neuman problems for the nd-order Seiberg-Witten equation on a compact -manifold admit a regular solution once the nonhomogeneous Palais-Smale condition 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 of configuration space. The coercivity of the -functional, when restricted into the Coulomb subspace, imply the existence of a weak solution. The regularity then follows from the boundedness of -norms of spinor solutions and the gauge fixing lemma.

  5. Towards parameter limits of displacement boundary value problems for Mohr-Coulomb models

    NARCIS (Netherlands)

    Rohe, A.

    2013-01-01

    To solve problems in geotechnical engineering often numerical methods such as the Finite Element Method (FEM) are used. This method can be applied for example for the calculation of the strength of dikes, the determination of the stability of (rail)road embankments, the prediction of deformations du

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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

  12. An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain

    Science.gov (United States)

    Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun

    2013-09-01

    In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt-Gram process (Arfken et al., 1985) [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the Mth-order iterative HAM by using each Mth-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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...

  19. 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.

  20. 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.

  1. Generalized form of boundary value problems method for material modeled as micro-polar media subjecting to the thermo-mechanical interaction

    Science.gov (United States)

    Zhang, Xiaomin; Zhang, Long; Chu, Zhongxiang; Peng, Song

    2016-09-01

    In this paper, the periodic structure material is modeled as the continuum homogeneous micro-polar media subjecting to thermo-mechanical interaction. Meanwhile, a series of equivalent quantities such as the equivalent stress, couple stress, displacement gradient and torsion tensor were defined by the integral forms of the boundary values of the external surface force, moment, displacement and the angular displacement, and were proved to satisfy the equivalence conditions of virtual work. Based on above works, the displacement boundary value problem was established to deduce the equivalent constitutive equation. Assume the representative volume element is composed of the spatial cross-framework, and applying the boundary value problem of displacement on frame structures, the equivalent elastic coefficients, temperature coefficients of equivalent stress and the temperature gradient coefficients of equivalent couple stress are deduced. In addition, themethod can also be extended to the stress boundary value problem to deduce the equivalent constitutive equation. The calculations indicate that the equivalent result can be obtained from the two kinds of boundary value problems.

  2. A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems

    Directory of Open Access Journals (Sweden)

    S. Djezzar

    2006-02-01

    Full Text Available We study a final value problem for first-order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition, we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.

  3. 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。

  4. 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.

  5. Examples of Systems of Functions Being Riesz Bases in L_{2}(0,1). Application to a Nonlinear Boundary Value Problem

    CERN Document Server

    Zhidkov, P E

    2001-01-01

    We establish examples of systems of functions being Riesz bases in L_{2}(0,1). We then apply this result to improve a theorem presented in [9] showing that an arbitrary "standard" system of solutions of a nonlinear boundary value problem, normalized to 1 in the same space, is a Riesz basis in this space. The proofs in this work are quite elementary.

  6. 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.

  7. 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.

  8. Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper, we study mixed elastico-plasticity problems in which part of the boundary is known, while the other part of the boundary is unknown and is a free boundary. Under certain conditions, this problem can be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundary value problem for complex equations. Using the theory of generalized analytic functions, the solvability of the problem is discussed.

  9. The Existence and Uniqueness of a New Boundary Value Problem (Type of Problem “E” for Linear System Equations of the Mixed Hyperbolic-Elliptic Type in the Multivariate Dimension with the Changing Time Direction

    Directory of Open Access Journals (Sweden)

    Mahammad A. Nurmammadov

    2015-01-01

    Full Text Available The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ε-regularizing” continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev space.

  10. THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATION ON SATURATED LAYERED SOIL SUBGRADE

    Institute of Scientific and Technical Information of China (English)

    陈胜立; 陈龙珠

    2002-01-01

    Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisvmmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition.The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numericad procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient Cv versus the dimensionless frequency ao are presented.

  11. Fucik spectrum,sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and some new results on the existence of nontrivial solutions,multiple solutions and sign-changing solutions are obtained.In one case seven nontrivial solutions are got.The techniques have independent interest.

  12. 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.

  13. Recursive Differentiation Method for Boundary Value Problems: Application to Analysis of a Beam-Column on an Elastic Foundation

    Directory of Open Access Journals (Sweden)

    Taha Mohamed

    2014-06-01

    Full Text Available In the present work, the recursive differentiation method (RDM is introduced and implemented to obtain analytical solutions for differential equations governing different types of boundary value prob- lems (BVP. Then, the method is applied to investigate the static behaviour of a beam-column resting on a two parameter foundation subjected to different types of lateral loading. The analytical solutions obtained using RDM and Adomian decomposition method (ADM are found similar but the RDM requires less mathematical effort. It is indicated that the RDM is reliable, straightforward and efficient for investigation of BVP in finite domains. Several examples are solved to describe the method and the obtained results reveal that the method is convenient for solving linear, nonlinear and higher order ordinary differential equations. However, it is indicated that, in the case of beam-columns resting on foundations, the beam-column may be buckled in a higher mode rather than a lower one, then the critical load in that case is that accompanies the higher mode. This result is very important to avoid static instability as it is widely common that the buckling load of the first buckling mode is always the smaller one, which is true only in the case of the beam-columns without foundations.

  14. Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussinesq Equations%二维非静力Boussinesq方程组的初边值问题

    Institute of Scientific and Technical Information of China (English)

    沈春; 孙梅娜

    2005-01-01

    Based on the theory of stratification, the well-posedness of the initial and boundary value problems for the system of two-dimensional non-hydrostatic Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for some representative initial and boundary value problems. Several special cases were discussed.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. On a character of the forced vibrations of two-layer plate in the second boundary value problem

    Directory of Open Access Journals (Sweden)

    Poghosyan H. M.

    2007-06-01

    Full Text Available The three-dimensional dynamic problem of the elasticity theory on forced vibration of orthotropic plate at coulomb friction between layers is solved by the asymptotic method. The bottom obverse surface is subject to external dynamic influences, and top - is rigidly fixed. The common asymptotic solution of the problem is found. The closed solution for particular type of problems is found. The resonance arising conditions are established. It is known, that constant tangential displacements acting to the second layer do not influence in stress-strain state of the first layer. It is shown, that the same phenomenon with the big accuracy remains in force at linearly varying on coordinates influences.

  5. 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

  6. 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.

  7. 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.

  8. 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.

  9. A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    Eugene O'Riordan; Jeanne Stynes; Martin Stynes

    2008-01-01

    A system of m (≥ 2) linear convection-diffusion two-point boundary value problems is examined, where the diffusion term in each equation is multiplied by a small parameter e and the equations are coupled through their convective and reactive terms via matrices B and A respectively. This system is in general singularly perturbed. Unlike the case of a single equation, it does not satisfy a conventional maximum princi-ple. Certain hypotheses are placed on the coupling matrices B and A that ensure exis-tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain; these hypotheses can be regarded as a strong form of diagonal dominance of B. This solution is decomposed into a sum of regular and layer components. Bounds are established on these compo-nents and their derivatives to show explicitly their dependence on the small parameterε. Finally, numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver-gent, uniformly in ε, to the true solution in the discrete maximum norm. Numerical results on Shishkin meshes are presented to support these theoretical bounds.

  10. 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.

  11. K调和函数的狄利克雷边值问题%Dirichlet's Boundary Value Problem for K-Harmonic Function

    Institute of Scientific and Technical Information of China (English)

    张建元

    2011-01-01

    In this paper,the Poisson integral is defined and studied within the elliptic domain B(0,ρ)(k)={z:|z(k)|≤ρ,0〈ρ〈+∞} to obtain the solutions of Dirichlet's and Schwarz's boundary value problem within K-harmonic function.The conclusion is the continuation and application of the corresponding results of the analytic function and harmonic function in the K-harmonic function.%在椭圆域B(0,ρ)(k)={z:|z(k)|≤ρ,0〈ρ〈+∞}上定义和讨论了泊松积分,并用它来求K-调和函数的狄利克雷和施瓦兹边值问题的解,所得结论是解析函数与调和函数的相应理论在K-解析(调和)函数中的继续和应用.

  12. PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL

    Institute of Scientific and Technical Information of China (English)

    Hussein A.H. Salem

    2011-01-01

    In this article, we investigate the existence of Pseudo solutions for some frac- tional order boundary value problem with integral boundary conditions in the Banach space of continuous function equipped with its weak topology. The class of such problems constitute a very interesting and important class of problems. They include two, three, multi-point and nonlocal boundary-value problems as special cases. In our investigation, the right hand side of the above problem is assumed to be Pettis integrable function. To encompass the full scope of this article, we give an example illustrating the main result.

  13. 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...

  14. 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.

  15. New formulations on the finite element method for boundary value problems with internal/external boundary layers; Novas formulacoes de elementos finitos para problemas de valor de contorno com camadas limite interna/externa

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Luis Carlos Martins

    1998-06-15

    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)

  16. 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。

  17. The Riemann-Hilbert Boundary Value Problem for General Elliptic Complex Equations of Second Order%二阶复椭圆 Riemann-Hilbert 边值问题

    Institute of Scientific and Technical Information of China (English)

    黄沙; 闻国椿

    2000-01-01

    This paper deals with the Riemann-Hilbert boundary value problem for general nonlinear elliptic complex equations of second order. Firstly we propose the Riemann-Hilbert problem and its well posedness, and then we give the representation of solutions for the modified boundary value problem and prove its solvability, and finally derive solvability conditions of the original Riemann-Hilbert problem.%讨论了一般二阶非线性椭圆复方程的Riemann-Hilbert边值问题. 首先给出Riemann-Hilbert问题及其适应性的概念,其次给出改进后的边值问题解的表述并证明了它的可解性,最后导出原Riemann-Hilbert边值问题的可解条件.

  18. STURM-LIOUVILLE PROBLEMS WITH EIGENDEPENDENT BOUNDARY AND TRANSMISSIONS CONDITIONS

    Institute of Scientific and Technical Information of China (English)

    Z. Akdo(g)an; M. Demirci; O.Sh. Mukhtarov

    2005-01-01

    The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem,which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

  19. 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.

  20. Positive Solutions of Singular Impulsive Emden-Fowler Boundary Value Problem with Negative Exponent%负指数的脉冲EMDEN-FOWLER方程奇异边值问题的正解

    Institute of Scientific and Technical Information of China (English)

    代丽美

    2007-01-01

    In this paper,we first give the method of lower and upper solutions for the existence of positive solutions to a singular impulsive boundary value problem by means of the fixed point theorem,then obtain a necessary and sufficient condition for the existence of positive solution of Emden-Fowler singular impulsive boundary value problem by using the method of lower and upper solutions.%利用不动点定理得到了脉冲奇异混合边值问题的上下解方法,并且利用此方法得到了负指数的脉冲Emden-Fowler方程奇异混合边值问题正解存在的充分必要条件.

  1. 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。

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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)

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 正指数超线性Emden-Fowler方程奇异边值问题的正解%Positive Solutions of Singular Boundary Value Problems ofPositive Exponent Superlinear Emden-Fowler Equations

    Institute of Scientific and Technical Information of China (English)

    毛安民

    2000-01-01

    This paper studies the existence of positivesolutions of singular boundary value problems of positive exponentsuperlinear Emden-Fowler equations. A necessary and sufficient conditionfor the existence of C1 [0,1] positive solutions is given by meansof function approximation with the fixed point theorems.%本文利用函数逼近和不动点理论给出了正指数超线性Emden-Fowler方程奇异边值问题有C1[0,1]正解的充分必要条件.

  17. Existence of Solutions of Boundary Value Problems for Forth Order Ordinary Differential Equations under Compactness Condition%紧型条件下四阶两点边值问题解的存在性

    Institute of Scientific and Technical Information of China (English)

    张栋

    2012-01-01

    Based on the fixed-point theorem and topological degree of condensing mapping,the existence and uniqueness of the solutions for boundary value problems of forth order differential equation in Banach space is proved precisely to calculate the spectral radius of linear operation and the measure of noncampactness.%通过对线性方程算子谱半径的论证及算子非紧性测度的讨论,利用凝聚场的拓扑度及不动点定理讨论了Banach空间四阶常微分方程边值问题解的存在性.

  18. 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.

  19. 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.

  20. 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...

  1. 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.

  2. 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)

  3. 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.

  4. 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.

  5. Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case

    Directory of Open Access Journals (Sweden)

    Georg S. Weiss

    2004-03-01

    Full Text Available We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.

  6. 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.

  7. 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.

  8. 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.

  9. NOVEL REGULARIZED BOUNDARY INTEGRAL EQUATIONS FOR POTENTIAL PLANE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    ZHANG Yao-ming; L(U) He-xiang; WANG Li-min

    2006-01-01

    The universal practices have been centralizing on the research of regularization to the direct boundary integal equations (DBIEs). The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundaryintegral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value (CPV) and Hadamard-finite-part (HFP) integrals are established for the plane potential problems.With some numerical results, it is shown that the better accuracy and higher efficiency,especially on the boundary, can be achieved by the present system.

  10. Moving boundary problems for the Harry Dym equation and its reciprocal associates

    Science.gov (United States)

    Rogers, Colin

    2015-12-01

    Moving boundary problems of generalised Stefan type are considered for the Harry Dym equation via a Painlevé II symmetry reduction. Exact solutions of such nonlinear boundary value problems are obtained in terms of Yablonski-Vorob'ev polynomials corresponding to an infinite sequence of values of the Painlevé II parameter. The action of two kinds of reciprocal transformation on the moving boundary problems is described.

  11. Solving Fluid Structure Interaction Problems with an Immersed Boundary Method

    Science.gov (United States)

    Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.

    2016-01-01

    An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.

  12. Millennial Values and Boundaries in the Classroom

    Science.gov (United States)

    Espinoza, Chip

    2012-01-01

    Students' relationships with authority and information are changing rapidly, and this presents a new set of interpersonal boundary challenges for faculty. The topic of setting boundaries often conjures up thoughts of how to protect oneself. The intent of this chapter is to explore how good rapport between teacher and student can be developed and…

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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...

  18. On a problem for wave equation with data on the whole boundary

    Science.gov (United States)

    Yessirkegenov, Nurgissa

    2016-08-01

    In this paper we propose a new formulation of boundary value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of boundary value problem in the classical and generalized senses. In order to substantiate the well-posedness of this problem it is necessary to have an effective representation of the general solution of the problem. In this direction we obtain a convenient representation of the general solution for the wave equation in a rectangular domain based on d'Alembert classical formula. The constructed general solution automatically satisfies the boundary conditions by a spatial variable. Further, by setting different boundary conditions according to temporary variable, we get some functional or functional-differential equations. Thus, the proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.

  19. 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.

  20. 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.

  1. 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.

  2. Biharmonic eigen-value problems and Lp estimates

    Directory of Open Access Journals (Sweden)

    Chaitan P. Gupta

    1990-01-01

    Full Text Available Biharmonic eigen-values arise in the study of static equilibrium of an elastic body which has been suitably secured at the boundary. This paper is concerned mainly with the existence of and Lp-estimates for the solutions of certain biharmonic boundary value problems which are related to the first eigen-values of the associated biharmonic operators. The methods used in this paper consist of the “a-priori” estimates due to Agmon-Douglas-Nirenberg and P. L. Lions along with the Fredholm theory for compact operators.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. On half inverse problem for differential pencils with the spectral parameter in boundary conditions

    Directory of Open Access Journals (Sweden)

    Sergey Buterin

    2011-08-01

    Full Text Available A second-order differential pencil on a finite interval with spectral parameter dependent boundary conditions is considered. The inverse problem is studied of recovering the coefficients of the boundary value problem from its spectrum, provided that on one half of the interval they are known a priori. The uniqueness theorem for this inverse problem is proved and a constructive procedure for finding its solution is obtained.

  10. 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

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. Prior Information in Inverse Boundary Problems

    DEFF Research Database (Denmark)

    Garde, Henrik

    of the method. Sparsity-based reconstruction is an iterative method, that through an optimization problem with a sparsity prior, approximates the inhomogeneities. Here we make use of prior information, that can cheaply be obtained from the monotonicity method, to improve both the contrast and resolution...

  19. Boundary integral methods for microfluidic problems

    Science.gov (United States)

    Burbidge, Adam

    2015-01-01

    Microscale experiments of reduced complexity allow one to tease out and examine some of the interesting phenomena that manifest in large hierarchically structured materials which are of general interest across many industries. Recent advances in high speed imaging techniques and post-processing allow experiments to yield small scale information which was previously unavailable, or extremely difficult to obtain. This additional information provides new challenges in terms of theoretical understanding and prediction that requires new tools. We discuss generalised weighted residual numerical methods as a means of solving physically derived systems of PDEs, using the steady Stokes equation as an example. These formulations require integration of arbitrary functions of submanifolds which often will have a lower dimensionality than the parent manifold, leading to cumbersome calculations of the Jacobian determinant. We provide a tensorial view of the transformation, in which the natural element coordinate system is a non-orthogonal frame, and derive an expression for the Jacobian factor in terms of the contravariant metric tensor gij. This approach has the additional advantage that it can be extended to yield the local surface curvature, which will be essential for correct implementation of free surface boundaries.

  20. The generalized solution of ill-posed boundary problem

    Institute of Scientific and Technical Information of China (English)

    CAO Weiping; MA Jipu

    2006-01-01

    In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk0,p(Ω, Σ). Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed. By utilizing the ideal of the generalized inverse of an operator, we introduce the generalized solution of the ill-posed boundary problem. Eventually, the connection between the generalized inverse and the generalized solution is studied. In this way, the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.

  1. 次线性Emden—Fowler方程两点边值问题的C[0,1]正解的唯一性%The uniqueness of the C[ 0,1 ] positive solution of the two-point boundary value problem of the sublinear Emden-Fowler equations

    Institute of Scientific and Technical Information of China (English)

    刘炳; 闫宝强

    2012-01-01

    Two-point boundary value problem of the sublinear Emden-Fowler equations has been addressed in many literatures, but the uniqueness of the C[0,1 ] positive solution has not been investigated. We employ monotone iterative method to address such problem and derive the uniqueness of the C[ 0,1 ] positive solution of the boundary value problem of such equations.%次线性Emden-Fowler方程两点边值问题在很多文献中用到,但对于该类问题的C[0,1]正解的唯一性还没有研究。本文利用单调迭代方法,对这一问题进行了研究,得出了该类方程两点边值问题的C[0,1]正解是存在且唯一的。

  2. ON BOUNDARY LAYER THE 3D PROBLEM ABOUT FORCED VIBRATIONS OF ORTHOTROPIC PLATE, FREELY-LYING ON THE RIGID FOUNDATION

    Directory of Open Access Journals (Sweden)

    Sargsyan M. Z.

    2009-12-01

    Full Text Available The problem of boundary layer of the orthotropic plate simply supported on the rigid foundation is considered, when on the upper plane of plate the normal load affects. The stressedly-deformed state boundary layer of plate is determined by using the asymptotic method. The damping of values for boundary layer are researched. The method of conjugation of the solutions of inner problem and of boundary layer is showed.

  3. Discontinuous Sturm-Liouville Problems with Eigenvalue Dependent Boundary Condition

    Energy Technology Data Exchange (ETDEWEB)

    Amirov, R. Kh., E-mail: emirov@cumhuriyet.edu.tr; Ozkan, A. S., E-mail: sozkan@cumhuriyet.edu.tr [Cumhuriyet University, Department of Mathematics Faculty of Art and Science (Turkey)

    2014-12-15

    In this study, an inverse problem for Sturm-Liouville differential operators with discontinuities is studied when an eigenparameter appears not only in the differential equation but it also appears in the boundary condition. Uniqueness theorems of inverse problems according to the Prüfer angle, the Weyl function and two different eigenvalues sets are proved.

  4. 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....

  5. 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....

  6. 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.

  7. 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

  8. Asymptotics of the solution to a singularly perturbed elliptic problem with a three-zone boundary layer

    Science.gov (United States)

    Beloshapko, V. A.; Butuzov, V. F.

    2016-08-01

    For a singularly perturbed elliptic boundary value problem, an asymptotic expansion of the boundary-layer solution is constructed and justified in the case when the boundary layer consists of three zones with different behavior of the solution, which is caused by the multiplicity of the root of the degenerate equation.

  9. Surface integrals approach to solution of some free boundary problems

    Directory of Open Access Journals (Sweden)

    Igor Malyshev

    1988-01-01

    Full Text Available Inverse problems in which it is required to determine the coefficients of an equation belong to the important class of ill-posed problems. Among these, of increasing significance, are problems with free boundaries. They can be found in a wide range of disciplines including medicine, materials engineering, control theory, etc. We apply the integral equations techniques, typical for parabolic inverse problems, to the solution of a generalized Stefan problem. The regularization of the corresponding system of nonlinear integral Volterra equations, as well as local existence, uniqueness, continuation of its solution, and several numerical experiments are discussed.

  10. Inverse Radiation Problem of Boundary Incident Radiation Heat Flux in Semitransparent Planar Slab with Semitransparent Boundaries

    Institute of Scientific and Technical Information of China (English)

    LiunLinhua; TanHeping; 等

    1998-01-01

    An inverse method is presented for estimating the unknown boundary incident radiation heat flux on one side of one-dimensional semitransparent planar slab with semitransparent boundaries from the knowledge of the radiation intensities exiting from the other side.The inverse problem is solved using conjugate gradient method of minimization based on discrete ordinates method(DOM) of radiative transfer equation.The equations of sensitivity coefficients are derived and easily solved by DOM,with the result that the complicated numerical differentiation commonly used in solving sensitivity coefficients is avoided.The effects of anisotropic scattering,absorption coefficient,scattering coefficient,boundary reflectivity,fluid temperature outside the boundaries,convection heat transfer coefficients,conduction coefficient of semitransparent media and slab thickness on the accuracy of the inverse analysis are investigated.The results show that the boundary incident radiation heat flux can be estimated accurately,even with noisy data.

  11. 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.

  12. Values of problem choice and communication

    DEFF Research Database (Denmark)

    Misfeldt, Morten; Willum Johansen, Mikkel

    choosing what problems to work on. These criteria include continuity to previous work, metacognitive considerations and a number of criteria relating to the values in both the larger mathematical community and smaller sub communities. The data shows that considerations about what other mathematicians...

  13. 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.

  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. 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.

  16. 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)

  17. 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

  18. 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 b...

  19. 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 b...

  20. 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

  1. 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...

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness. PMID:27006888

  7. 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...

  8. 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...

  9. 一类三阶常微分方程非线性三点边值问题解的存在性%Existence of Solutions of a Nonlinear Three-Point Boundary Value Problem for Third-Order Ordinary Differential Equations

    Institute of Scientific and Technical Information of China (English)

    沈建和; 周哲彦; 余赞平

    2009-01-01

    In this paper,existence of solutions of third-order differential equationy (t) = f(t,y(t),y'(t),y"(t))with nonlinear three-point boundary condition g(y(a),y'(a),y"(a)) = 0,h(y(b),y'(b))=0,I(y(c),y'(c),y"(c)) = 0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a,b,c ∈ R,a < b< c; f:[a,c] × R3a → R,g:R3 → R,h:R2→R and I:R3 → Rare continuous functions.The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem.As an application,an example with an explicit solution is given to demonstrate the validity of the results in this paper.

  10. 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.

  11. 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.

  12. THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Sun Haitao; Wang Yuanhan

    2007-01-01

    A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network (IRBFN) constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations (BIE) can be established while the fundamental solutions to the problems are introduced. The singular value decomposition (SVD) method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available.In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.

  13. 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.

  14. 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。

  15. 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

  16. 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...

  17. THEORETICAL RELATIONS OF BOUNDARY DISPLACEMENT DERIVATIVES AND TRACTIONS AT SINGULAR BOUNDARY POINT FOR 2D ISOTROPIC ELASTIC PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    Zailiang Li; Cheng Wang

    2008-01-01

    Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point,there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point.The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work.By using the relations,positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori.Therefore,more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed.A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.

  18. WELL-POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INVISCID COMPRESSIBLE ADIABATIC FLUID

    Institute of Scientific and Technical Information of China (English)

    WANG Yue-peng

    2005-01-01

    The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local (exact) solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.

  19. 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.

  20. Solution of MHD problems with mixed-type boundary conditions

    Energy Technology Data Exchange (ETDEWEB)

    Antimirov, M.IA.

    1985-06-01

    The introduction of artificial anisotropy of the dynamic viscosity in one of the subregions in which the solution is sought is utilized to derive an approximation method for MHD problems with mixed-type boundary conditions. The method is demonstrated through two problems: slow rotation of a disk and motion of a finite-width infinitely long plate in an infinite volume of a conducting fluid. The velocity and magnetic field solutions are obtained in the form of integrals of Bessel functions, and the torque is found. It is shown that when the Hartmann number approaches infinity the torque of a convex body of revolution in a longitudinal magnetic field is equal to that of a disk lying at the centerline section of the body.

  1. SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.

  2. BOUNDARY ELEMENT ANALYSIS OF CONTACT PROBLEMS USING ARTIFICIAL BOUNDARY NODE APPROACH

    Institute of Scientific and Technical Information of China (English)

    Bahattin KANBER; Ibrahim H. GUZELBEY; Ahmet ERKLI

    2003-01-01

    An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.

  3. 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.

  4. 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...

  5. 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.

  6. 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

  7. 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.

  8. Finite difference method of first boundary problem for quasilinear parabolic systems ( Ⅳ)——Convergence of iteration

    Institute of Scientific and Technical Information of China (English)

    周毓麟; 沈隆钧; 袁光伟

    1997-01-01

    More work is done to study the explicit, weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system:where u, , and f are m-dimensional vector valued functions, A is an m × m positively definite matrix, and ut = For this problem, the convergence of iteration for the general difference schemes is proved.

  9. 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.

  10. Existence and uniqueness of solutions of nonlinear two-point boundary value problems for fourth order differential equations%四阶微分方程非线性两点边值问题解的存在唯一性

    Institute of Scientific and Technical Information of China (English)

    高永馨; 谢燕华

    2012-01-01

    利用上下解方法,讨论了四阶微分方程非线性两点边值问题y(4) =f(x,y,y′,y″,y(′″)),y(b) =b0,y′(b) =b1,y″(b) =h(y″(a)),g(y(a),y(b),y′(a),y′(b),y″(a),y″(b),y(′″)(a),y(′″)(b)) =0解的存在唯一性.%By using the method of upper - lower solution,the existence and uniquenss of solutions of nonlinear two -point boundary value problems for fourth order differential equation y(4) =f(x,y,y′,y″,y(′″)),y(b) =b0,y′(b) =b1,y″(b) =h(y″(a)),g(y(a),y(b),y′(a),y′(b),y″(a),y″(b),y(′″)(a),y(′″)(b)) =0 are investigated.

  11. 具有变号非线性项的奇异三点边值问题正解的存在性和不存在性%The Nonexistence and Existence of Singular Three-point Boundary Value Problems with Sign-changing Nonlinearities

    Institute of Scientific and Technical Information of China (English)

    闫宝强

    2011-01-01

    This paper discusses singular three-point boundary value problems y″(t) + a(t)f (t, y(t), y′(t)) = 0, 0 < t< 1, y′(0) = 0, y(1) = αy(η),where 0 < α < 1, 0 <η < 1, f changes sign and may be singular at y = 0 and y′ = 0%该文讨论奇异三点边值问题y"(t)+a(t)f(t,y(t),y'(t))=0,0<t<1,y'(0)=0,y(1)=αy(η)正解的存在与不存在性,这里0<α<1,0<η<1,f变号且在y=0和y'=0具有奇异性.

  12. 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。

  13. Singular integral equations boundary problems of function theory and their application to mathematical physics

    CERN Document Server

    Muskhelishvili, N I

    2011-01-01

    Singular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics.This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problem

  14. 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.

  15. 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.

  16. 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.

  17. 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

  18. 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.

  19. Scrap Value Functions in Dynamic Decision Problems

    NARCIS (Netherlands)

    Ikefuji, M.; Laeven, R.J.A.; Magnus, J.R.; Muris, C.H.M.

    2010-01-01

    We introduce an accurate, easily implementable, and fast algorithm to compute optimal decisions in discrete-time long-horizon welfaremaximizing problems. The algorithm is useful when interest is only in the decisions up to period T, where T is small. It relies on a flexible parametrization of the re

  20. 非线性2n阶微分方程的非线性两点边值问题解的存在性%Existence of solutions to nonlinear two-point boundary value problems for 2nth-order nonlinear differential equation

    Institute of Scientific and Technical Information of China (English)

    高永馨; 谢燕华

    2009-01-01

    利用上下解的方法研究了非线性2n阶常微分方程Y~((2n))=f(t,y,y',…,y~((2n-1))满足如下边界条件条件g_0(y(a),y'(a))=0,g_1(y'(a),y"(a),…,y~((2n-3))(a))=0,g_2(y~((2n-2))(a),y~((2n-1))(a))=0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),Y(i+1)(c))=0(i=3,4,…,2n-2).的非线性两点边值问题解的存在性.%By using the method of upper-lower solutions,the sufficient conditions are given for the existence of solutions to nonlinear two point boundary value problems for nonlinear 2nth-order differential equation y~((2n))=f(t,y,y',...,y~((2n-1))) with the boundary conditions g_0(y(a),y'(a)) =0,g_1(y'(a),y"(a),...,y~((2n-3))(a)) =0,g_2(y~((2n-2))(a),y~((2n-1))(a)) =0,h_0(y(c),y'(c),y"(c))=0,h_i(y~((i))(c),y~((i+1))(c))=0(i=3,4,...,2n-2).