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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. Boundary value problems and partial differential equations

    CERN Document Server

    Powers, David L

    2005-01-01

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

  3. 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...

  4. Semigroups, boundary value problems and Markov processes

    CERN Document Server

    Taira, Kazuaki

    2014-01-01

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

  5. 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.

  6. 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.

  7. Unique solution to periodic boundary value problems

    Directory of Open Access Journals (Sweden)

    Yong Sun

    1991-01-01

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

  8. 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.

  9. 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.

  10. Boundary Value Problem for Black Rings

    CERN Document Server

    Morisawa, Yoshiyuki; Yasui, Yukinori

    2007-01-01

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

  11. Geodesic boundary value problems with symmetry

    OpenAIRE

    Cotter, Colin; Holm, Darryl

    2010-01-01

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

  12. Boundary value problems and medical imaging

    International Nuclear Information System (INIS)

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

  13. 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.

  14. 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...

  15. Complementary Lidstone Interpolation and Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2009-01-01

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

  16. Spectral integration of linear boundary value problems

    CERN Document Server

    Viswanath, Divakar

    2012-01-01

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

  17. Geodesic boundary value problems with symmetry

    CERN Document Server

    Cotter, C J

    2009-01-01

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

  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. 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 $T$.

  20. 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...

  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. 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...

  3. 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.

  4. 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.

  5. 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

  6. Boundary value problems and Markov processes

    CERN Document Server

    Taira, Kazuaki

    2009-01-01

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

  7. Positive Solutions for Boundary Value Problems with Fractional Order

    Directory of Open Access Journals (Sweden)

    Mouffak Benchohra

    2013-02-01

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

  8. 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.

  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 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.

  11. 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.

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

    Science.gov (United States)

    Sancho, M.

    1980-01-01

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

  13. 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.

  14. Solvability for fractional order boundary value problems at resonance

    OpenAIRE

    Hu Zhigang; Liu Wenbin

    2011-01-01

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

  15. 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.

  16. 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.

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

    Science.gov (United States)

    Gu, Longfei

    2014-01-01

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

  18. 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...

  19. Linear boundary value problems for differential algebraic equations

    OpenAIRE

    Balla, Katalin; März, Roswitha

    2003-01-01

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

  20. 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.

  1. 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.

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

    International Nuclear Information System (INIS)

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

  3. Solution of Boundary-Value Problems using Kantorovich Method

    Science.gov (United States)

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

    2016-02-01

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

  4. 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.

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

    International Nuclear Information System (INIS)

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

  6. 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.

  7. 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

  8. 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...

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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...

  17. 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.

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

    Directory of Open Access Journals (Sweden)

    Topal SGulsan

    2009-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Liu Yuji

    2008-01-01

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

  20. 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.

  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. 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.

  4. 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.

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

    Institute of Scientific and Technical Information of China (English)

    Chen Guowang; Xue Hongxia

    2008-01-01

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

  6. The boundary value problems for the scalar Oseen equation

    Czech Academy of Sciences Publication Activity Database

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

    2012-01-01

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

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

    International Nuclear Information System (INIS)

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

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

    International Nuclear Information System (INIS)

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

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

    Czech Academy of Sciences Publication Activity Database

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

    2003-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Paul A. Binding

    1997-01-01

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

  11. 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.

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

    Directory of Open Access Journals (Sweden)

    Michela Palmucci

    2001-01-01

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

  13. 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.

  14. 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.

  15. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

    2005-01-01

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

  17. 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

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

    OpenAIRE

    Torres, Francisco J.

    2013-01-01

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

  19. 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.

  20. 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.

  1. 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.

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

    Directory of Open Access Journals (Sweden)

    Safia Benmansour

    2011-09-01

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

  3. 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.

  4. 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

  5. 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.

  6. 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.

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

    Science.gov (United States)

    Soldatov, Alexander P.; Zhura, Nikolay A.

    2015-11-01

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

  8. 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.

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

    International Nuclear Information System (INIS)

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

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

    Directory of Open Access Journals (Sweden)

    Chaitan P. Gupta

    1989-01-01

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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

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

    International Nuclear Information System (INIS)

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

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  1. 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...

  2. 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...

  3. 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.

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

    International Nuclear Information System (INIS)

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

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

    International Nuclear Information System (INIS)

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2008-05-15

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

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

    International Nuclear Information System (INIS)

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

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

    International Nuclear Information System (INIS)

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

  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. 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.

  11. 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.

  12. 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.

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

    Directory of Open Access Journals (Sweden)

    Tomasz Drwięga

    2007-01-01

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

  14. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Kiguradze, I.; Půža, Bedřich

    2005-01-01

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

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

    Directory of Open Access Journals (Sweden)

    George L. Karakostas

    2000-06-01

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

  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 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.

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

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

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

  20. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

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

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

    OpenAIRE

    Liu, Jian

    2015-01-01

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

  3. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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 .

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

    CERN Document Server

    Sieber, Jan

    2010-01-01

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

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

    OpenAIRE

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

    2011-01-01

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

  12. 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

  13. 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.

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

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    1989-01-01

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

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

    CERN Document Server

    Chang, Tongkeun; Yang, Minsuk

    2011-01-01

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

  16. 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.

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

    OpenAIRE

    Çetin, Muhammed; Sezer, Mehmet; Kocayiğit, Hüseyin

    2015-01-01

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

  18. 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.

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

    OpenAIRE

    Chandler-Wilde, SN

    1994-01-01

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

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

    International Nuclear Information System (INIS)

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

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

    Directory of Open Access Journals (Sweden)

    Kovalenko A. V.

    2013-12-01

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

  2. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Malaguti, L.

    2003-01-01

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

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

    OpenAIRE

    Chaitan P. Gupta

    1991-01-01

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

  5. 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.

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

    Directory of Open Access Journals (Sweden)

    Jingliang Qiu

    2012-08-01

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

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

    Directory of Open Access Journals (Sweden)

    Weihua JIANG

    2015-04-01

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

  8. 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...

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

    Directory of Open Access Journals (Sweden)

    Assia Guezane-Lakoud

    2010-09-01

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

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

    OpenAIRE

    Vorotnikov, Dmitry A.

    2009-01-01

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

  11. 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.

  12. 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.

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

    Directory of Open Access Journals (Sweden)

    Yang Xiao-Jun

    2015-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Andrei V. Faminskii

    2010-01-01

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

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

    DEFF Research Database (Denmark)

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

    2014-01-01

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

  16. 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

  17. 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.

  18. 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.

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

    International Nuclear Information System (INIS)

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

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

    Directory of Open Access Journals (Sweden)

    Zhiyong Wang

    2008-09-01

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

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

    Directory of Open Access Journals (Sweden)

    Olivier Sarbach

    2012-08-01

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

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

    Directory of Open Access Journals (Sweden)

    Tvrdý Milan

    2001-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Muzammal Iftikhar

    2013-01-01

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

  4. 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.

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

    International Nuclear Information System (INIS)

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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

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

    Directory of Open Access Journals (Sweden)

    Ravi P. Agarwal

    2006-01-01

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

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

    OpenAIRE

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

    2008-01-01

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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

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

    Directory of Open Access Journals (Sweden)

    Yujun Cui

    2006-03-01

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

  19. 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)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1977-01-01

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

  1. 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.

  2. 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.

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

    CERN Document Server

    Nakonechnyi, Olexandr; Shestopalov, Yury

    2009-01-01

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

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

    Science.gov (United States)

    Roul, Pradip

    2016-04-01

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

  5. 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.

  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 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).

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

    International Nuclear Information System (INIS)

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

  9. 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.

  10. 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.

  11. 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...

  12. 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.

  13. 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 ...

  14. 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.

  15. 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.

  16. 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.

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

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

    OpenAIRE

    Martin Eggensperger; Kaufmann, Eric R.; Nickolai Kosmatov

    2004-01-01

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

  19. 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.

  20. 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.

  1. 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'

  2. 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]...

  3. 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.

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

    Science.gov (United States)

    Ying, Wenjun; Henriquez, Craig S.

    2007-12-01

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

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

    International Nuclear Information System (INIS)

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

  6. 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.

  7. 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.

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

    Directory of Open Access Journals (Sweden)

    R. P. Kanwal

    1985-06-01

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

  9. 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.

  10. 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.)

  11. 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.

  12. 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.

  13. 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.

  14. 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.

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

    International Nuclear Information System (INIS)

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

  16. 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.

  17. 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.

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

    Directory of Open Access Journals (Sweden)

    M. Venkatesulu

    1995-12-01

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

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

    Czech Academy of Sciences Publication Activity Database

    Vodstrčil, Petr

    2004-01-01

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

  20. 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.

  1. 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.

  2. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Babuška, I.; Chleboun, Jan

    2002-01-01

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

  4. 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.

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

    OpenAIRE

    Prigarin, Sergej M.; Winkler, Gerhard

    2003-01-01

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

  6. 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.

  7. 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.

  8. 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.

  9. 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.

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

    International Nuclear Information System (INIS)

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

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

    OpenAIRE

    Otero Juez, Jesús

    1987-01-01

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

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

    Directory of Open Access Journals (Sweden)

    John R. Graef

    2013-01-01

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

  13. 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.

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2010-12-20

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

  15. 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.

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

    OpenAIRE

    Liang Yue; Yang He

    2011-01-01

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

  17. 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...

  18. 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.

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

    Directory of Open Access Journals (Sweden)

    Zhang Peiguo

    2011-01-01

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

  20. 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

  1. 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.

  2. 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.

  3. 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].

  4. 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.

  5. 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.

  6. 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.

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

    Directory of Open Access Journals (Sweden)

    Hua Luo

    2005-02-01

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

  8. 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.

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

    OpenAIRE

    1997-01-01

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

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

    CERN Document Server

    Henkin, Gennadi M

    2011-01-01

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

  11. 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.

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

    Institute of Scientific and Technical Information of China (English)

    刘其林; 莫嘉琪

    2001-01-01

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

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

    Directory of Open Access Journals (Sweden)

    В.П. Денисюк

    2009-02-01

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

  14. 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

  15. 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.

  16. 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 $u=0$.

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

    International Nuclear Information System (INIS)

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

  18. 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.

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

    OpenAIRE

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

    2007-01-01

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

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

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

    OpenAIRE

    Yan Sun

    2015-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Alberto Cabada

    1994-01-01

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

  8. 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.

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

    Directory of Open Access Journals (Sweden)

    Winkert Patrick

    2010-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Driss Seghir

    2001-11-01

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

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

    OpenAIRE

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

    2015-01-01

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

  12. 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.

  13. 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

  14. 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

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

    Science.gov (United States)

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

    2013-05-01

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

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

    DEFF Research Database (Denmark)

    Grubb, Gerd

    2011-01-01

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

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

    CERN Document Server

    Dauge, Monique

    1988-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Khasambiev Mokhammad Vakhaevich

    2014-07-01

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

  19. 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...

  20. 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.

  1. 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.

  2. 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.

  3. 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...

  4. 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.

  5. 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.

  6. 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.

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

    Science.gov (United States)

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

    2016-06-01

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

  8. 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.

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

    International Nuclear Information System (INIS)

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

  10. 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.

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

    International Nuclear Information System (INIS)

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

  12. 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.

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

    Directory of Open Access Journals (Sweden)

    Nguyen Manh Hung

    2008-03-01

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

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

    Institute of Scientific and Technical Information of China (English)

    罗李平

    2014-01-01

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

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

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    2002-01-01

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

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

    Czech Academy of Sciences Publication Activity Database

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

    2004-01-01

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

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

    OpenAIRE

    Gennaro Infante

    2005-01-01

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

  18. 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.

  19. 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.

  20. 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.

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

    OpenAIRE

    Li Yongkun; Shu Jiangye

    2011-01-01

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

  2. 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.

  3. 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.

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

    Directory of Open Access Journals (Sweden)

    George L. Karakostas

    2006-08-01

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

  5. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Samoilenko, A. M.

    2007-01-01

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

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

    International Nuclear Information System (INIS)

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

  8. 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.

  9. 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.

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

    OpenAIRE

    Staněk Svatoslav

    2010-01-01

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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    2001-01-01

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

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

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Šremr, Jiří

    2006-01-01

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

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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。

  5. 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。

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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...

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Solvability of a nonlinear boundary value problem

    Directory of Open Access Journals (Sweden)

    S. Peres

    2013-01-01

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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

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

    DEFF Research Database (Denmark)

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

    2010-01-01

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

  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. 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。

  12. 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.

  13. Nonresonance conditions for fourth order nonlinear boundary value problems

    OpenAIRE

    F. Munyamarere; C. Fabry; De Coster, C.

    1994-01-01

    This paper is devoted to the study of the problemu(4)=f(t,u,u′,u″,u‴),u(0)=u(2À),   u′(0)=u′(2À),   u″(0)=u″(2À),   u‴(0)=u‴(2À).We assume that f can be written under the formf(t,u,u′,u″,u‴)=f2(t,u,u′,u″,u‴)u″+f1(t,u,u′,u″,u‴)u′+f0(t,u,u′,u″,u‴)u+r(t,u,u′,u″,u‴)where r is a bounded function. We obtain existence c...

  14. Positive solutions and singular discrete boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Cecchi, M.; Došlá, Zuzana; Marini, M.

    2004-01-01

    Roč. 4, - (2004), s. 271-283. ISSN 1085-3375 Institutional research plan: CEZ:AV0Z1019905 Keywords : second - order nonlinear difference equation * singular nonlinearities * decaying solution Subject RIV: BA - General Mathematics

  15. Preconditioning of boundary value problems using elementwise Schur complements

    Czech Academy of Sciences Publication Activity Database

    Axelsson, Owe; Blaheta, Radim; Neytcheva, M.

    2009-01-01

    Roč. 31, č. 2 (2009), s. 767-789. ISSN 0895-4798 Institutional research plan: CEZ:AV0Z30860518 Keywords : preconditioning methods * multilevel methods * two-by-two block partitioning Subject RIV: BA - General Mathematics Impact factor: 2.411, year: 2009 http://dx.doi.org/10.1137/070679673

  16. On numerical-analytic techniques for boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Shchobak, N.

    2012-01-01

    Roč. 12, č. 3 (2012), s. 5-10. ISSN 1335-8243 Institutional support: RVO:67985840 Keywords : numerical-analytic method * periodic successive approximations * Lyapunov-Schmidt method Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/aeei.2012.12.issue-3/v10198-012-0035-1/v10198-012-0035-1.xml?format=INT

  17. RBF Multiscale Collocation for Second Order Elliptic Boundary Value Problems

    KAUST Repository

    Farrell, Patricio

    2013-01-01

    In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multilevel fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations. © 2013 Society for Industrial and Applied Mathematics.

  18. 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.

  19. 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.

  20. 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.

  1. Boundary values as Hamiltonian variables: new Poisson brackets

    International Nuclear Information System (INIS)

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

  2. An efficient computer based wavelets approximation method to solve Fuzzy boundary value differential equations

    Science.gov (United States)

    Alam Khan, Najeeb; Razzaq, Oyoon Abdul

    2016-03-01

    In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.

  3. 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

  4. 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.

  5. 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

  6. A Computational Study of the Boundary Value Methods and the Block Unification Methods for ${y}^{?}=f(x,y,{y}^{\\prime })$

    OpenAIRE

    Biala, T. A.

    2016-01-01

    We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency.

  7. Blended General Linear Methods based on Boundary Value Methods in the GBDF family

    CERN Document Server

    Brugnano, Luigi

    2010-01-01

    Among the methods for solving ODE-IVPs, the class of General Linear Methods (GLMs) is able to encompass most of them, ranging from Linear Multistep Formulae (LMF) to RK formulae. Moreover, it is possible to obtain methods able to overcome typical drawbacks of the previous classes of methods. For example, order barriers for stable LMF and the problem of order reduction for RK methods. Nevertheless, these goals are usually achieved at the price of a higher computational cost. Consequently, many efforts have been made in order to derive GLMs with particular features, to be exploited for their efficient implementation. In recent years, the derivation of GLMs from particular Boundary Value Methods (BVMs), namely the family of Generalized BDF (GBDF), has been proposed for the numerical solution of stiff ODE-IVPs. In particular, this approach has been recently developed, resulting in a new family of L-stable GLMs of arbitrarily high order, whose theory is here completed and fully worked-out. Moreover, for each one o...

  8. Automated Test Data Generation Based On Individual Constraints and Boundary Value

    Directory of Open Access Journals (Sweden)

    Hitesh Tahbildar

    2010-09-01

    Full Text Available Testing is an important activity in software development. Unfortunately till today testing is done manually by most of the industry due to high cost and complexity of automation. Automated testing can reduce the cost of software significantly. Automated Software Test Data Generation is an activity that in the course of software testing automatically generates test data for the software under test. Most of the automated test data generation uses constraint solver to generate test data. But it cannot generate test data when the constraints are not solvable. Although method can be found to generate test data even if the constraints are unsolvable, but it is poor in terms of code coverage. In this paper, we propose a test data generation method to improve test coverage and to avoid the unsolvable constraints problem. Our method is based on the individual constraints and same or dependent variable to create the path table which holds the information about the path traversed by various input test data. For generating unique test data for all the linearly independent feasible path we created equivalence class from the path table on the basis of path traversed by the various input test data. The input data is taken based on individual constraints or boundary value. Our results are compared with cyclomatic complexity and number of possible infeasible paths. The comparison shows the effectiveness of our method.

  9. Boundary Values for Regional to Continental Scale Greenhouse Gas Flux Estimation

    Science.gov (United States)

    Andrews, A. E.; Basu, S.; Benmergui, J. S.; Dlugokencky, E. J.; Karion, A.; Masarie, K. A.; Michalak, A. M.; Mountain, M. E.; Nehrkorn, T.; Stein, A. F.; Sweeney, C.; Tans, P. P.; Thoning, K. W.; Trudeau, M.; Yadav, V.

    2015-12-01

    Errors in prescribed boundary values can bias estimates of surface fluxes in data-assimilation and inverse modeling studies of regional greenhouse gas budgets. Sensitivity to boundary value errors is particularly important for CO2, since strong seasonally opposing fluxes result in comparatively small net annual uptake. We have developed empirical boundary value products for North America for CO2, CH4, N2O and other long-lived gases using data from aircraft profiles and marine boundary layer sites in NOAA's Global Greenhouse Gas Reference Network. The influence of each aircraft sample is mapped forward and backward from the measurement location using trajectories generated with NOAA's HYSPLIT model driven by meteorological fields from the North American Regional Reanalysis system. These data and influence functions are used to create free-tropospheric reference surfaces that describe monthly scale variability as a function of longitude, latitude, altitude, and time. Data from remote marine boundary layer sites are used to generate Atlantic and Pacific marine boundary layer reference surfaces that vary with latitude, altitude and time. Taken together, the free-troposphere and marine boundary layer reference surfaces provide 4-dimensional boundary values for the continent. This product has been significantly improved compared to earlier versions used in several published studies. We have also developed a related framework for simultaneous optimization of boundary values and surface fluxes in the NOAA CarbonTracker-Lagrange regional inverse modeling system, which uses surface and boundary value footprints from the WRF-STILT model. In this case, we adjust a prior estimate for the boundary values such as can be obtained from the global Eulerian CarbonTracker modeling system or another global model. Vertically resolved data from aircraft and/or from a combination of surface and column measurements are needed to reliably separate surface and boundary influences. We will

  10. Spaces of boundary values related to a multipoint version of the KP-hierarchy

    NARCIS (Netherlands)

    Helminck, G.F.

    2004-01-01

    In this paper one considers a finite number of points in the complex plane and various spaces of boundary values on circles surrounding these points. To this geometric configuration one associates a Grassmann manifolds that is shown to yield solutions of a multipoint version of the linearization of

  11. Strang-type preconditioners for solving fractional diffusion equations by boundary value methods

    NARCIS (Netherlands)

    Gu, Xian-Ming; Huang, Ting-Zhu; Zhao, Xi-Le; Li, Hou-Biao; Li, Liang

    2015-01-01

    The finite difference scheme with the shifted Grünwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with initial values. Recently, boundary value method (BVM) was develop

  12. 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.

  13. Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems

    OpenAIRE

    Dimovski, Ivan; Tsankov, Yulian

    2011-01-01

    Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с изп...

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

    Directory of Open Access Journals (Sweden)

    Cabada Alberto

    2006-01-01

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

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

    Directory of Open Access Journals (Sweden)

    2006-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Boubakeur Merouani

    2015-07-01

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

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

    OpenAIRE

    Boubakeur Merouani; Razika Boufenouche

    2015-01-01

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

  18. Nonmonotone Impulse Effects in Second-Order Periodic Boundary Value Problems

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    New York : Hindawi Publishing Corporation, 2004 - (Siafarikas, P.), s. 323-336 ISBN 977-5945-14-3. [International Conference on Differential , Difference Equation s and Their Applications. Patras (GR), 01.07.2002-05.07.2002] R&D Projects: GA ČR(CZ) GA201/01/1199 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order nonlinear ordinary differential equation with impulses * periodic solutions * lower and upper functions Subject RIV: BA - General Mathematics

  19. Nonmonotone impulse effects in second-order periodic boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    2004-01-01

    Roč. 7, - (2004), s. 577-590. ISSN 1085-3375 R&D Projects: GA ČR GA201/01/1199 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order nonlinear ordinary differential equation with impulses * periodic solutions * lower and upper functions Subject RIV: BA - General Mathematics

  20. Method of lower and upper functions in impulsive periodic boundary value problems

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Tvrdý, Milan

    Singapore : World Scientific Publishing, 2005 - (Dumortier, F.; Broer, H.; Mawhin, J.), s. 252-257 ISBN 981-256-169-2. [Equadiff 2003, International Conference on Differential Equation s. Hasselt 2003 (DE), 22.07.2003-26.07.2003] R&D Projects: GA ČR(CZ) GA201/01/1199 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order nonlinear ordinary differential equation with impulses * periodic solutions * lower and upper functions Subject RIV: BA - General Mathematics

  1. 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.

  2. Magnetostatic boundary-value problems in the incomplete-nonlinear formulation and methods of their solution

    International Nuclear Information System (INIS)

    A new class preconditioners for one class of two-or three-dimensional elliptic operators with highly varying coefficients is developed. The construction is based on domain decomposition method when the substructure contains internal cross points. The approximation of the initial equation is based on the Galerkin method for special subspaces of Sobolev's spaces H1. The general estimates of the condition number for the preconditioned operator are given. This number does not depend on the variation range of the coefficient of the initial operator and slightly (logarithmically) depends on a step of the domain triangulation. The preconditioner operators provide means for constructing the cost-effective methods for solution of magnetostatic equations in incomplete-nonlinear formulation as well as in formulation of the Maxwell equation for the scale potential representation. These operators are easily inverible both for parallel and for traditional computing achitectures. 36 refs.; 1 tab

  3. Asymptotic investigation of the nonlinear boundary value dynamic problem for the systems with finite sizes

    International Nuclear Information System (INIS)

    Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions

  4. 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.

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

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan

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

  6. Study of the stability of solutions of some classes of initial boundary value problems of aerohydroelasticity

    International Nuclear Information System (INIS)

    The stability of several classes of constructions containing elastic elements has been studied. A nonlinear mathematical model of a vibration equipment device intended for the intensification of technological processes, for example, the stirring process, has been considered as an example

  7. Impulsive Periodic Boundary Value Problems for Dynamic Equations on Time Scale

    Directory of Open Access Journals (Sweden)

    Eric R. Kaufmann

    2009-01-01

    Full Text Available Let 𝕋 be a periodic time scale with period p such that 0,ti,T=mp∈𝕋, i=1,2,…,n, m∈ℕ, and 0

  8. 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.

  9. 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.

  10. Introduction to partial differential equations from Fourier series to boundary-value problems

    CERN Document Server

    Broman, Arne

    2010-01-01

    This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

  11. Approximate solution of the boundary value problem for a nonlinear heat equation with a nonlinear source

    International Nuclear Information System (INIS)

    A nonlinear heat equation with a nonlinear source is considered. The parameters at which an approximate solution can be constructed in the form of a propagating thermal front have been determined. Exact solutions in some cases have been obtained

  12. Bifurcations of cycles and tori in one boundary value problem for the nonlocal equation of erosion

    International Nuclear Information System (INIS)

    A partial differential equation with deviating spatial variables has been considered. The case of small deviations has been studied. It has been shown that spatially inhomogeneous solutions can be sought as bifurcating solutions from homogeneous equilibrium states and that the wavelength of the corresponding solutions depends almost only on one parameter, the magnitude of deviation

  13. 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.

  14. Neuman boundary value problems defined and solved on domains with uncertain boundary

    Czech Academy of Sciences Publication Activity Database

    Chleboun, Jan; Babuška, I.

    Bratislava : Slovak University of Technology, 1999 - (Bock, I.; Zajac, M.), s. 3-5 [Workshop on Functional Analysis and its Applications in Mathematical Physics and Optimal Control /2./. Nemecká (SK), 13.09.1999-18.09.1999] R&D Projects: GA ČR GA201/97/0217; GA MŠk ME 148 Subject RIV: BA - General Mathematics

  15. A quasi-boundary value method for regularizing nonlinear ill-posed problems

    Directory of Open Access Journals (Sweden)

    Dang Duc Trong

    2009-09-01

    Full Text Available In this article, a modified quasi-boudary regularization method for solving nonlinear backward heat equation is given. Sharp error estimates for the approximate solutions, and numerical examples to illustrate the effectiveness our method are provided. This work extends to the nonlinear case earlier results by the authors [33,34] and by Clark and Oppenheimer [6].

  16. A constructive approach to boundary value problems with state-dependent impulses

    Czech Academy of Sciences Publication Activity Database

    Rachůnková, I.; Rachůnek, L.; Rontó, András; Rontó, M.

    2016-01-01

    Roč. 274, February (2016), s. 726-744. ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : non-linear system of differential equation * impulse effect * parameterization * successive approximations Subject RIV: BA - General Mathematics Impact factor: 1.551, year: 2014 http://www.sciencedirect.com/science/article/pii/S0096300315015234

  17. 一类Dirichlet边值逆问题%A CLASS OF INVERSE DIRICHLET BOUNDARY VALUE PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    王明华

    2008-01-01

    给出解析函数的一类Dirichlet边值逆问题的数学提法.依据解析函数Dirichlet边值问题和广义Dirichlet边值问题的理论,讨论了此边值逆问题的可解性.利用解析函数Dirichlet边值问题的Schwarz公式,给出了该边值逆问题的可解条件和解的表示式.

  18. A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

    Directory of Open Access Journals (Sweden)

    TIAN Jialei

    2015-11-01

    Full Text Available By using the ground as the boundary, Molodensky problem usually gets the solution in form of series. Higher order terms reflect the correction between a smooth surface and the ground boundary. Application difficulties arise from not only computational complexity and stability maintenance, but also data-intensiveness. Therefore, in this paper, starting from the application of external gravity disturbance, Green formula is used on digital terrain surface. In the case of ignoring the influence of horizontal component of the integral, the expression formula of external disturbance potential determined by boundary value consisted of ground gravity anomalies and height anomaly difference are obtained, whose kernel function is reciprocal of distance and Poisson core respectively. With this method, there is no need of continuation of ground data. And kernel function is concise, and suitable for the stochastic computation of external disturbing gravity field.

  19. Accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior measurements, I. Boundary-value techniques

    CERN Document Server

    Plaster, B

    2013-01-01

    We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar potential will satisfy a Laplace equation. Therefore, if either the vector field components or the normal derivative of the scalar potential can be measured on the surface of this boundary, thus defining a Dirichlet or Neumann boundary-value problem, respectively, the interior vector field components or the scalar potential (and, thus, the field components via the gradient of the potential) can be uniquely determined via solution of the Laplace equation. We discuss the applicability of this technique to the determination of the interior magnetic field components during the operating phase of neutron electric dipole moment experim...

  20. Boundary values of mixed-symmetry massless fields in AdS space

    CERN Document Server

    Chekmenev, Alexander

    2015-01-01

    We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal gauge fields subject to the invariant equations. As a byproduct our approach gives a manifestly conformal and gauge covariant formulation for these fields. Although such formulation employs numerous auxiliary fields, it comes with a systematic procedure for their elimination that results in a more concise formulation involving only a reasonable set of auxiliaries, which eventually (at least in principle) can be reduced to the minimal formulation in terms of the irreducible Lorentz tensors. The simplest mixed-symmetry field, namely, the rank-3 tensor associated to the two-row Young diagram, is considered in some details.

  1. Strang-type preconditioners for solving fractional diffusion equations by boundary value methods

    OpenAIRE

    Gu, Xian-Ming; Huang, Ting-Zhu; Zhao, Xi-Le; Li, Hou-Biao; Li, Liang

    2013-01-01

    The finite difference scheme with the shifted Gr\\"{u}nwarld formula is employed to semi-discrete the fractional diffusion equations. This spatial discretization can reduce to the large system of ordinary differential equations (ODEs) with initial values. Recently, boundary value method (BVM) was developed as a popular algorithm for solving large systems of ODEs. This method requires the solutions of one or more nonsymmetric, large and sparse linear systems. In this paper, the GMRES method wit...

  2. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations

    OpenAIRE

    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 ...

  3. Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

    Science.gov (United States)

    Jawerth, Bjoern; Sweldens, Wim

    1993-01-01

    We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

  4. Boundary-value approach to nuclear effects in muon-catalyzed d-t fusion

    International Nuclear Information System (INIS)

    The use of boundary-matching techniques, as contained in R-matrix theory, to describe multichannel nuclear reactions is discussed. After giving a brief summary of the application of such techniques to the nuclear reactions in the 5He system, we discuss a simple extension of the description to include muons, which was used to calculate nuclear effects on the L = O eigenvalues of the dtμ molecule in various adiabatic approximations. Next, the form of the outgoing nαμ wavefunction is discussed, resulting in a new formulation of the amplitudes used to calculate the α-μ sticking fraction. Possible methods of solving for these amplitudes using the boundary-value approach are suggested, and some deficiencies of the ''standard'' expression for the sticking amplitudes are pointed out. 3 figs., 3 tabs

  5. On Perturbation Solutions for Axisymmetric Bending Boundary Values of a Deep Thin Spherical Shell

    Directory of Open Access Journals (Sweden)

    Rong Xiao

    2014-01-01

    Full Text Available On the basis of the general theory of elastic thin shells and the Kirchhoff-Love hypothesis, a fundamental equation for a thin shell under the moment theory is established. In this study, the author derives Reissner’s equation with a transverse shear force Q1 and the displacement component w. These basic unknown quantities are derived considering the axisymmetry of the deep, thin spherical shell and manage to constitute a boundary value question of axisymmetric bending of the deep thin spherical shell under boundary conditions. The asymptotic solution is obtained by the composite expansion method. At the end of this paper, to prove the correctness and accuracy of the derivation, an example is given to compare the numerical solution by ANSYS and the perturbation solution. Meanwhile, the effects of material and geometric parameters on the nonlinear response of axisymmetric deep thin spherical shell under uniform external pressure are also analyzed in this paper.

  6. 一类非线性周期边值问题在共振情况下解的存在性%The Existence of Solution for a Certain Nonlinear Periodic Boundary Value under the Condition of Resonance

    Institute of Scientific and Technical Information of China (English)

    吴春晨

    2011-01-01

    本文考虑一个非线性周期边值问题的解的存在性,利用迭合度中的Mawhin延拓定理证明该问题解的存在性。%This paper focuses on the existence of solution for a nonlinear periodic boundary value problem.By making use of the Mawhin continuation theorem of coincidence degree,the author proves the existence of solutions for the problem.

  7. THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.

  8. Sensitivity requirements for accessing interior magnetic field vector components in neutron electric dipole moment experiments via exterior boundary-value measurements

    International Nuclear Information System (INIS)

    We study the sensitivity requirements for determining the vector components of the magnetic field in the interior regions of electric dipole moment experiments via exterior boundary-value measurements. The basic concept for our method is as follows. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be defined such that its interior encloses no currents or sources of magnetization, each of the interior vector field components and the magnetic scalar potential will satisfy a Laplace equation. Therefore, if either the vector field components or the normal derivative of the scalar potential can be measured on the surface of this boundary, thus defining a Dirichlet or Neumann boundary-value problem, respectively, the interior vector field components or the scalar potential (and, thus, the field components via the gradient of the potential) can be uniquely determined via solution of the Laplace equation. We discuss the applicability of this technique to the determination of the interior magnetic field components during the operating phase of neutron electric dipole moment experiments when it is not, in general, feasible to perform direct in situ measurements of the interior field components. We then study the specifications that a vector field probe must satisfy in order to determine the interior vector field components to a certain precision

  9. On solvability of a three-point boundary value problem for second order nonlinear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Vodstrčil, Petr

    2007-01-01

    Roč. 40, č. 1 (2007), s. 55-65. ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order nonlinear functional differential equation * three-point BVP Subject RIV: BA - General Mathematics

  10. 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.

  11. Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrodinger Equation

    Institute of Scientific and Technical Information of China (English)

    辛杰

    2008-01-01

    @@ It is well known that Feynman and Hibbs[1] used path integrals over Brownian paths to derive the standard(nonfractional) Schrodinger equation. Recently, Laskin[5, 6] showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known Schrodinger equation, then the path integral over Lévy trajectories leads to the fractional Schrodinger equation. Laskin[7] showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu[4] studied some physical applications of the fractional Schrodinger equation.

  12. Two-point boundary value problems for strongly singular higher-order linear differential equations with deviating arguments

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Partsvania, N.

    -, č. 38 (2012), s. 1-34 ISSN 1417-3875 Institutional research plan: CEZ:AV0Z10190503 Keywords : higher order differential equation * linear * deviating argument Subject RIV: BA - General Mathematics Impact factor: 0.740, year: 2012 http://www.emis.de/journals/EJQTDE/p1045. pdf

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

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.

    2013-01-01

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

  14. On finfing solutions of two-point boundary value problems for a class of non-linear functional differential systems

    Czech Academy of Sciences Publication Activity Database

    Rontó, András; Rontó, M.; Shchobak, N.

    2012-01-01

    Roč. 13, May 04 (2012), s. 1-17 ISSN 1417-3875. [Colloquium on the Qualitative Theory of Differential Equations /9./. Szeged, 28.06.2011-01.07.2011] Institutional research plan: CEZ:AV0Z10190503 Keywords : functional differential equation * two-point conditions * successive approximations Subject RIV: BA - General Math ematics Impact factor: 0.740, year: 2012 http://www. math .u-szeged.hu/ejqtde/periodica.html?periodica=3¶mtipus_ertek=publications¶m_ertek=-1

  15. A boundary value problem for the spherically symmetric motion of a pressureless gas with a temperature-dependent viscosity

    Czech Academy of Sciences Publication Activity Database

    Ducomet, B.; Nečasová, Šárka

    2009-01-01

    Roč. 32, č. 16 (2009), s. 2071-2101. ISSN 0170-4214 R&D Projects: GA ČR GA201/08/0012 Institutional research plan: CEZ:AV0Z10190503 Keywords : spherically symmetric motion * pressureless gas * temperature-dependent viscosity Subject RIV: BA - General Mathematics Impact factor: 0.808, year: 2009

  16. On the basis property of eigenfunctions of boundary value problems for second-order fractional differential equations

    International Nuclear Information System (INIS)

    It has been proven that the operator generated by the differential expression of the second order with a fractional derivative in a lower term does not generate associated functions and that the system of the eigenfunctions of this operator forms a basis L2(0, 1)

  17. 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.

  18. A General Formulation of the Postulate for Minimum Volume of the MHD Generator Duct with Fixed Outer Boundary Values

    International Nuclear Information System (INIS)

    The most important data for describing the influence of the MHD expansion group (consisting of nozzle, duct and diffuser) on the characteristic parameters of the overall cycle, in particular on the overall efficiency, are the thermodynamic-state quantities at the entrance of the nozzle and at the exit of the diffuser, ''the outer boundary values''. With these data unchanged, variation of the shape of the expansion line does not affect the overall performance of the process. Therefore the question arises which expansion shape is best from the point of view of an MHD generator, if the outer boundary values are fixed,or, in general, as a function of the outer boundary values. As the generator duct is the most complicated and, especially with the magnet, the most expensive element of the expansion group, minimizing of the duct volume is a reasonable criterion to be applied in the determination of the expansion shape. The paper shows how this criterion leads to a simple differential relationship between the electrical conductivity of the working gas, the gas velocity and the cross-section of the channel. If this relationship is used to complete the system of differential equations governing the energy conversion process, the resulting expansion shape is optimal with respect to minimum duct volume. Usually a somewhat arbitrary condition is taken to determine the expansion shape, e. g. the gas velocity or Mach number is postulated to be constant. There are some optimization procedures known in the literature which, however, refer to either the inlet or the outlet state of the duct, i.e. only one point of the expansion line falls on the optimum line. These computations are included as special cases in the more general treatment of the present paper. Finally an example is calculated for the MHD expansion under consideration of the optimization criterion. (author)

  19. Thermal creep problems by the discrete Boltzmann equation

    Directory of Open Access Journals (Sweden)

    L. Preziosi

    1991-05-01

    Full Text Available This paper deals with an initial-boundary value problem for the discrete Boltzmann equation confined between two moving walls at different temperature. A model suitable for the quantitative analysis of the initial boundary value problem and the relative existence theorem are given.

  20. A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

    Institute of Scientific and Technical Information of China (English)

    Wang Geng

    2006-01-01

    A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

  1. THE SINGULARLY PERTURBED PROBLEM FOR COMBUSTION REACTION DIFFUSION

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2001-01-01

    A singularly perturbed combustion reaction diffusion Robin boundary value problem is considered. Using the theory of differential ineaqality, the existence of solution to the problem is proved and the asymptotic estimation of the solution is obtained.

  2. On solution of the integral equations for the potential problems of two circular-strips

    Directory of Open Access Journals (Sweden)

    C. Sampath

    1988-01-01

    Dirichlet and Newmann boundary value problems of two equal infinite coaxial circular strips in various branches of potential theory. For illustration, these solutions are applied to solve some boundary value problems in electrostatics, hydrodynamics, and expressions for the physical quantities of interest are derived.

  3. 一个方程组的解及相关边值问题%The solution of a Equation System and the Boundary Value Problem for It

    Institute of Scientific and Technical Information of China (English)

    李玉成

    2000-01-01

    该文考虑方程组t((e)u/(e)x-(e)u/(e)y-(e)ω/(e)t)+ω=0 (e)u/(e)y=-(e)v/(e)x,(e)u/(e)t=-(e)ω/(e)x,(e)v/(e)t=(e)ω/(e)y}的解f=u+iv+jt∈C2,找到(H)可解的一个充要条件,并讨论相关边值问题解的存在性和积分表示,推广了1992年H.Leutwiler[1]的结果.

  4. 关于(k,n-k)共轭边值问题的Green函数%Green's Function of (k,n-k) Conjugate Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    胡卫敏; 谷丽

    2006-01-01

    主要给出了(k,n-k)共轭边值问题{(-1)(n-k)y(n-k)=ξ(t),0<t<1 y(i)(0)=0,0≤i≤k-1 y(j)(0)=0,0≤j≤n-k-1 ξ(t)∈C[0,1]且在(0,1)上ξ(t)>0的唯一正解y(t)=∫10G(t,s)ξ(s)ds(0≤t≤1)中Green函数G(t,s)的构造式为G(t,s)={tk(1-s)k/(k-1)!(n-k-1)!n-k-1∑j=0 Cjn-k-1[t(1-s)]j/(k+j)(s-t)n-k-1-j,0≤t≤s≤1(2)(1-t)n-kSn-k/(k-1)!(n-k-1)!k-1∑j=0 Cjk-1[S(1-t)]j/n-k+j(t-s)-1-j,0≤s≤s≤1

  5. 一类两点边值问题的多重非负解%Multiple Nonnegative Solutions for a Class of Two-point Boundary Value Problems

    Institute of Scientific and Technical Information of China (English)

    程建纲

    2005-01-01

    该文考虑两点边值问题[1/q(t)][q(t)y'(t)]'+p(t)f(y(t))=0,λ1 y(α)-λ2 y'(α)( 0),y(β)=B非负解的存在性,其中p(t)可能在t=α或t=β附近具有奇异性,f(0)≥0,lim/y→+∞f(y)/y=+∞,并且存在y>0,使得f(y)<0.

  6. Multiresolution Data Analysis - Numerical Realization by use of Domain Decomposition Methods and Fast Multipole Techniques / Multiscale Solutions of Oblique Boundary-Value Problems by Layer Potentials

    OpenAIRE

    Freeden, W.; Mayer, C.

    2002-01-01

    This survey paper deals with multiresolution analysis from geodetically relevant data and its numerical realization for functions harmonic outside a (Bjerhammar) sphere inside the Earth. Harmonic wavelets are introduced within a suit- able framework of a Sobolev-like Hilbert space. Scaling functions and wavelets are defined by means of convolutions. A pyramid scheme provides efficient implementation und economical computation. Essential tools are the multiplicative Schwarz alternating algorit...

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

    Science.gov (United States)

    Dymarskii, Ya M.; Evtushenko, Yu A.

    2016-05-01

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

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

    Directory of Open Access Journals (Sweden)

    Yuji Liu

    2003-12-01

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

  9. 分数阶微分包含反周期边值问题解的存在性%Existence of Solutions for Fractional-order Differential Inclusion with Anti-periodic Boundary Value Conditions

    Institute of Scientific and Technical Information of China (English)

    齐悦

    2014-01-01

    In this paper , we investigate the following fractional order differential inclusion with anti-periodic boundary value problems cDαy(t)∈F(t,y(t)),t∈[0,T],T>0,2<α≤3, y(0)=-y(T), cDpy(0)=-cDpy(T),cDqy(0)=-cDqy(T), new criteria are established based on fixed-point theorem .Our results extend some known single value problem to multi-value conditions .%利用不动点定理,研究了带有反周期边值分数阶微分包含问题cDαy(t)∈F(t,y(t)),t∈[0,T],T>0,2<α≤3, y(0)=-y(T),cDpy(0)=-cDpy(T),cDqy(0)=-cDqy(T),解的存在性,所得结果将已有的单值结果推广到多值情形。

  10. Beyond the standard. Decree on Sensitive Locations, boundary values and public health; De norm voorbij. Besluit Gevoelige Bestemmingen, grenswaarden en de gezondheid

    Energy Technology Data Exchange (ETDEWEB)

    Van de Weerdt, R. [GGD, Hulpverlening Gelderland Midden, Arnhem (Netherlands); Van Itegem, S. [Gemeente Harderwijk, Harderwijk (Netherlands)

    2009-12-15

    On 10 September 2009, the Dutch municipality of Harderwijk established its Environmental Policy Plan 2009-2012. Remarkably, the policy with regard to sensitive locations has been formulated more strictly than prescribed by the Decree on sensitive locations. The authors believe that Harderwijk is the first municipality to take the boundary values for PM10 and NO2 one step further in their decisions on whether or not to allow new sensitive locations in the vicinity of national roads and provincial roads. [Dutch] Op 10 september 2009 heeft de gemeente Harderwijk haar Milieubeleidsplan 2009-2012 vastgesteld. Opmerkelijk is dat het beleid ten aanzien van gevoelige bestemmingen scherper is geformuleerd dan het Besluit Gevoelige Bestemmingen voorschrijft. De auteurs geloven dat Harderwijk de eerste gemeente is die verdergaat dan de grenswaarden voor PM10 en NO2 bij het al dan niet toestaan van nieuwe gevoelige bestemmingen in de nabijheid van rijkswegen en provinciale wegen.

  11. 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.

  12. 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.

  13. 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.

  14. Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪; 韩祥临

    2003-01-01

    The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.

  15. Renormalization group in mathematical physics and some problems of laser optics

    International Nuclear Information System (INIS)

    An original approach to constructing special type symmetries for boundary value problems, renormgroup symmetries, is reviewed. It is applied to a system of geometric optics equations. New solutions to the laser beam self-focusing problem are presented

  16. Higher order Nevanlinna functions and the inverse three spectra problem

    OpenAIRE

    Olga Boyko; Olga Martinyuk; Vyacheslav Pivovarchik

    2016-01-01

    The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on \\([0,a]\\), the Dirichlet-Dirichlet problem on \\([0,a/2]\\) and the Neumann-Dirichlet problem on \\([a/2,a]\\) is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.

  17. Convergence theorems for intermediate problems. II

    OpenAIRE

    Beattie, C. A.; Greenlee, W. M.

    2002-01-01

    Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundary-value problems and atomic problems. In addition, we prove convergence of the T*T method of Bazley and Fox without an alignment of projections hypothesis required in previous literature.

  18. Numerical methods for hyperbolic differential functional problems

    Directory of Open Access Journals (Sweden)

    Roman Ciarski

    2008-01-01

    Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.

  19. Factorization, Riemann-Hilbert problems and the corona problem

    CERN Document Server

    Camara, M C; Karlovich, Yu I; Spitkovsky, I M

    2011-01-01

    The solvability of the Riemann-Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener-Hopf type factorization with bounded outer factors but rather general diagonal elements of its middle factor. This covers, in particular, the almost periodic setting. Connections with the corona problem are discussed. Based on those, constructive factorization criteria are derived for several types of triangular 2-by-2 matrices.

  20. 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.

  1. Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian

    OpenAIRE

    Pasquale Candito; Giuseppina D'Aguí

    2014-01-01

    In this paper, we investigate the existence of constant-sign solutions for a nonlinear Neumann boundary value problem involving the discrete \\(p\\)-Laplacian. Our approach is based on an abstract local minimum theorem and truncation techniques.

  2. On the solvability of Dirichlet problem for the weighted p-Laplacian

    OpenAIRE

    Ewa Szlachtowska

    2012-01-01

    The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \\(p\\)-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.

  3. Positive Solutions of a Second-OrderThree-point Boundary Value Problem

    Institute of Scientific and Technical Information of China (English)

    李兆兴; 张中新

    2002-01-01

    The existence of positive solutions is established for a nonlinear second-order three-point boundary value problem. The result improves and extends the main result in Electron J. Differential Equations, 34(1999), 1-8.

  4. The linear theory of functional differential equations: existence theorems and the problem of pointwise completeness of the solutions

    International Nuclear Information System (INIS)

    A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.

  5. Spectral problems from quantum field theory

    OpenAIRE

    Dmitri V. Vassilevich

    2004-01-01

    We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern developments in quantum field theory and strings and show which new spectral and boundary value problems arise.

  6. ON A PROBLEM OF E. REICH

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    In 1981, E. Reich established a theorem which stated a sufficient condition for a quasiconformal mapping to be a unique extremal mapping with the given boundary value, and asked whether or not such a uniquely extremal mapping was a Teichmuller mapping in his remark. In this paper, the above open problem was solved and consequently the theorem was strengthened.

  7. Semidefinite linear complementarity problems

    International Nuclear Information System (INIS)

    Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.)

  8. Asymptotic behaviour of the div-curl problem in exterior domains

    OpenAIRE

    Neudert, Michael; von Wahl, Wolf

    2001-01-01

    We study the variety of solutions of the inhomogeneous div--curl problem in exterior domains in dependence on the decay conditions on div and curl. Here we consider the Neumann as well as the Dirichlet boundary value prescription where in the first case the topological impact is decisive. In the second case the integrability conditions on div, curl and the boundary values are more difficult. Finally we present Hölder estimates for the solution of the Dirichlet or Neumann proble...

  9. Evolution problems in materials with fading memory

    Directory of Open Access Journals (Sweden)

    Sandra Carillo

    2007-12-01

    Full Text Available Evolution problems in materials with memory are here considered.Thus, linear integro-differential equations with Volterra type kernel areinvestigated. Specifically, initial boundary value problems are studied;physical properties of the material under investigation are shown to induce the choice of a suitable function space, where solutions are looked for. Then, combination with the application of Fourier transforms, allows to prove existence and uniquenes of the solution. Indeed, the original evolution problem is related to an elliptic one: existence and uniqueness results are proved for the latter and, thus, for the original problem. Two different evolution initial boundary value problems with memory which arise, in turn, in the framework of linear heat conduction and of linear viscoelasticity are compared.

  10. A BEM FOR TRANSIENT HEAT CONDUCTION PROBLEM OF ANISOTROPIC FGM

    OpenAIRE

    Azis, Mohammad Ivan

    2014-01-01

    A boundary element method (BEM) for the solution of a certain class of nonlinear parabolic initial boundary value problems for a certain class of anisotropic functionally graded media is derived. The method is then used to obtain numerical values for some particular transient 2-D heat conduction problems for anisotropic functionally graded materials (FGM).

  11. Regularity of spectral fractional Dirichlet and Neumann problems

    DEFF Research Database (Denmark)

    Grubb, Gerd

    2016-01-01

    Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of . Recalling the results on complex powers and complex interpolation of domains of elliptic boundary value problems by Seeley in...... the various Dirichlet- and Neumann-type boundary problems associated with the fractional Laplacian....

  12. On the Role of Diffusion Behaviors in Stability Criterion for p-Laplace Dynamical Equations with Infinite Delay and Partial Fuzzy Parameters under Dirichlet Boundary Value

    OpenAIRE

    Ruofeng Rao; Zhilin Pu; Shouming Zhong; Jialin Huang

    2013-01-01

    By the way of Lyapunov-Krasovskii functional approach and some variational methods in the Sobolev space ${W}_{0}^{1,p}\\left(Ω\\right)$ , a global asymptotical stability criterion for p-Laplace partial differential equations with partial fuzzy parameters is derived under Dirichlet boundary condition, which gives a positive answer to an open problem proposed in some related literatures. Different from many previous related literatures, the nonlinear p-Laplace diffusion item plays its role in the...

  13. Evolution problems in materials with fading memory

    OpenAIRE

    Sandra Carillo

    2007-01-01

    Evolution problems in materials with memory are here considered.Thus, linear integro-differential equations with Volterra type kernel areinvestigated. Specifically, initial boundary value problems are studied;physical properties of the material under investigation are shown to induce the choice of a suitable function space, where solutions are looked for. Then, combination with the application of Fourier transforms, allows to prove existence and uniquenes of the solution. Indeed, the original ...

  14. 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.

  15. 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.

  16. 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.

  17. A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2003-01-01

    A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered.Under suitable conditions,by using the theory of differential inequalities,the asymptotic behavior of solutions for the initial boundary value problems are studied,reduced problems of which possess two intersecting solutions.

  18. Variational method of solution of the inverse problem of quantum mechanics potential definition

    International Nuclear Information System (INIS)

    Methods of variational calculation were used for solution of the inverse problem of quantum mechanics potential definition in linear and quasilinear Schroedinger equations. The necessary condition, satisfied by solution of the problem, was found. Its correctness and correctness of the boundary-value problem at assigned potentials were investigated

  19. Numerical solution of pipe flow problems for generalized Newtonian fluids

    International Nuclear Information System (INIS)

    In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)

  20. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    DEFF Research Database (Denmark)

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari;

    2010-01-01

    Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... boundary value problems, but also are used as mathematical models in viscoelastic and inelastic flows. The purpose of this paper is to present the application of the homotopy-perturbation method (HPM) and variational iteration method (VIM) to solve some boundary value problems in structural engineering...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...

  1. Qualitative properties of solutions to elliptic singular problems

    OpenAIRE

    Gladiali F; Porru G; Berhanu S

    1999-01-01

    We investigate the singular boundary value problem in , on , where . For , we find the estimate where depends on only, denotes the distance from to and is suitable constant. For , we prove that the function is concave whenever is convex. A similar result is well known for the equation , with . For , and we prove convexity sharpness results.

  2. A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR EXTERIOR 3-D PROBLEM

    Institute of Scientific and Technical Information of China (English)

    De-hao Yu; Ji-ming Wu; Ji-ming Wu

    2001-01-01

    In this paper, a nonoverlapping domain decomposition method, which is based on the natural boundary reduction(cf. [4, 13, 15]), is developed to solve the boundary value problem in exterior three-dimensional domain of general shape. Convergence analyses both for the exterior spherical domain and the general exterior domain are made. Some numerical examples are also provided to illustrate the method.

  3. Existence of solutions for fractional-order differential inclusion with integral boundary value problems%带有积分边值条件的分数阶微分包含解的存在性

    Institute of Scientific and Technical Information of China (English)

    杨丹丹

    2015-01-01

    分数阶微分方程被广泛用于解决众多领域的工程问题,如新材料科学、流体力学、电子电路等.此外,在生物学、经济学、最优控制等学科通过建立微分包含模型,对一些实际问题进行理论分析和研究,近年来,有关带有边值条件的分数阶微分方程和分数阶微分包含的研究受到了广泛关注.对基于CABADA和WANG的一类分数阶微分方程正解的存在性进行了研究,将其单值结果推广到多值情形.利用多值映射的不动点定理,研究了如下带有积分边值条件的分数阶微分包含问题:CD0+ay(t)∈F(t,y(t)),t∈(0,1),α∈(2,3),y(0)=y'(0)=0,y(1)=λ∫10y(s)ds,得到了包含非线性项是凸和非凸2种情形的带有积分边值条件的分数阶微分包含解存在的充分条件.

  4. Banach空间中发展方程的反周期边值问题%Anti-periodic Boundary Value Problem for a Class of Evolution Equation in Banach Space

    Institute of Scientific and Technical Information of China (English)

    张育梅; 程毅; 王靖华

    2012-01-01

    利用同伦方法证明了一类发展方程反周期解在Banach空间中的存在性和唯一性.先构造同伦方程,再对方程做先验估计.最后通过定义解算子,运用拓扑度方法,给出了发展方程反周期解存在的充分条件.%We proved the existence and uniqueness of a class of evolution equation in Banach space using homotopy methods. We constructed a homotopy equation and made α priori, estimate to this equation. Under the definition solution operator conditions, a sufficient condition of existence of solutions was obtained by means of topological degree method.

  5. 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。

  6. 解Riemann-Liouville分数阶导数微分方程两点边值问题%Solving Two-Point Boundary Value Problems of Fractional Differential Equations with Riemann-Liouville Derivatives

    Institute of Scientific and Technical Information of China (English)

    聂宁明; 赵艳敏; Salvador Jiménez; 李敏; 唐贻发; Luis Vázquez

    2010-01-01

    研究了两类含Riemann-Liouville分数阶导数的分数阶微分方程两点边值问题.理论上,通过引入分数阶Green函数将含有Riemann-Liouville分数阶导数的两点边值问题等价转换成一个积分方程;并用Lipschitz条件和压缩映射原理给出了含有Riemann-Liouville分数阶导数的两点边值问题的解存在唯一的充分条件;数值上,设计了单打靶法,把含Riemann-Liouville分数阶导数的两点边值问题转化为含Riemann-Liouville分数阶导数的初值问题进行求解,并给出了较为精确的数值解.仿真结果表明:单打靶法是数值求解此类分数阶微分方程两点边值问题的有效工具.

  7. 二维静态场域边值问题数值解法的MATLAB实现%MATLAB REALIZATION ON THE ARITHMETIC SOLUTION METHOD OF BOUNDARY VALUE PROBLEMS FOR TWO-DIMENSION STATIC FIELDS

    Institute of Scientific and Technical Information of China (English)

    何红雨; 保宗悌

    2003-01-01

    介绍了计算二维静态场边值问题的有限差分法和有限单元法,并用MATLAB对其进行了数值求解,由此体现出MATLAB在二维静态场域边值问题数值求解中的优越性.

  8. Impulsive Boundary Value Problem for Nonlinear Differential Equations of Fractional Order%非线性分数阶微分方程的脉冲边值问题

    Institute of Scientific and Technical Information of China (English)

    薛妮娜

    2012-01-01

    本文利用Altman's不动点定理和Leray-Schauders不动点定理证明了一类含积分边值条件的非线性脉冲分数阶微分方程解的存在性,同时给出了一个例子来说明主要结果.

  9. Solving Initial and Boundary Value Problems for Heat Conduction Equations by Spherical Bessel Functions%利用球Bessel函数求解热传导方程的定解问题

    Institute of Scientific and Technical Information of China (English)

    程炜

    2015-01-01

    讨论一个球形区域上的球对称热传导方程的定解问题,目标是建立用球Bessel函数为特征函数的级数解.采用分离变量法借助于球Bessel函数及其性质求出所研究问题级数解的表达式.

  10. Continuous boundary values of conformal maps

    OpenAIRE

    Qiu, Zhijian

    2013-01-01

    Let $G$ be a bounded simply connected domain in the complex plane. A point $a\\in \\partial G$ is said to be accessible from inside of $G$ if there is a Jordan arc $J$ such that $J\\subset \\bar G$ and $J\\cap\\partial G=\\{a\\}$. In this paper the author shows that a univalent analytic function $\\psi$ from the unit disk $D$ onto $G$ extends continuously to $\\bar D$ if and only if every $a\\in\\partial G$ is accessible. The main result covers a famous theorem proved by C. Carathe\\"{o}dory, which says t...

  11. Partial differential equations theory and completely solved problems

    CERN Document Server

    Hillen, Thomas; van Roessel, Henry

    2014-01-01

    Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin

  12. MODIFIED LEAST SQUARE METHOD ON COMPUTING DIRICHLET PROBLEMS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    The singularity theory of dynamical systems is linked to the numerical computation of boundary value problems of differential equations. It turns out to be a modified least square method for a calculation of variational problem defined on Ck(Ω), in which the base functions are polynomials and the computation of problems is transferred to compute the coefficients of the base functions. The theoretical treatment and some simple examples are provided for understanding the modification procedure of the metho...

  13. 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.

  14. 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.

  15. Vector-valued measure and the necessary conditions for the optimal control problems of linear systems

    International Nuclear Information System (INIS)

    The vector-valued measure defined by the well-posed linear boundary value problems is discussed. The maximum principle of the optimal control problem with non-convex constraint is proved by using the vector-valued measure. Especially, the necessary conditions of the optimal control of elliptic systems is derived without the convexity of the control domain and the cost function. (author)

  16. 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.

  17. 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)

  18. Domain decomposition method for solving elliptic problems in unbounded domains

    International Nuclear Information System (INIS)

    Computational aspects of the box domain decomposition (DD) method for solving boundary value problems in an unbounded domain are discussed. A new variant of the DD-method for elliptic problems in unbounded domains is suggested. It is based on the partitioning of an unbounded domain adapted to the given asymptotic decay of an unknown function at infinity. The comparison of computational expenditures is given for boundary integral method and the suggested DD-algorithm. 29 refs.; 2 figs.; 2 tabs

  19. POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    By the Schauder fixed point theory,this paper establishes the existence of positive solutions to a(k,n k) m-point boundary value problem.We show that there exists a positive constant b such that the problem has at least one positive solution when the homogeneous boundary parameter is smaller than b,and no positive solution when this parameter is greater than b.

  20. The stability for the Cauchy problem for elliptic equations

    CERN Document Server

    Alessandrini, Giovanni; Rosset, Edi; Vessella, Sergio

    2009-01-01

    We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.

  1. Worldtube conservation laws for the null-timelike evolution problem

    CERN Document Server

    Winicour, Jeffrey

    2011-01-01

    I treat the worldtube constraints which arise in the null-timelike initial-boundary value problem for the Bondi-Sachs formulation of Einstein's equations. Boundary data on a worldtube and initial data on an outgoing null hypersurface determine the exterior spacetime by integration along the outgoing null geodsics. The worldtube constraints are a set of conservation laws which impose conditions on the integration constants. I show how these constraints lead to a well-posed initial value problem governing the extrinsic curvature of the worldtube, whose components are related to the integration constants. Possible applications to gravitational waveform extraction and to the well-posedness of the null-timelike initial-boundary value problem are discussed.

  2. Variational approximation of flux in conforming finite element methods for elliptic partial differential equations: a model problem

    OpenAIRE

    Brezzi, Franco; Hughes, T.J.R.; Suli, Endre

    2001-01-01

    We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.

  3. Global stability for the multi-channel Gel'fand-Calder\\'on inverse problem in two dimensions

    CERN Document Server

    Santacesaria, Matteo

    2011-01-01

    We prove a global logarithmic stability estimate for the multi-channel Gel'fand-Calder\\'on inverse problem on a two-dimensional bounded domain, i.e. the inverse boundary value problem for the equation $-\\Delta \\psi + v\\, \\psi = 0$ on $D$, where $v$ is a smooth matrix-valued potential defined on a bounded planar domain $D$.

  4. Eigenvalue problems for fractional ordinary differential equations

    International Nuclear Information System (INIS)

    The eigenvalue problems are considered for the fractional ordinary differential equations with different classes of boundary conditions including the Dirichlet, Neumann, Robin boundary conditions and the periodic boundary condition. The eigenvalues and eigenfunctions are characterized in terms of the Mittag–Leffler functions. The eigenvalues of several specified boundary value problems are calculated by using MATLAB subroutine for the Mittag–Leffler functions. When the order is taken as the value 2, our results degenerate to the classical ones of the second-ordered differential equations. When the order α satisfies 1 < α < 2 the eigenvalues can be finitely many.

  5. Boundary and eigenvalue problems in mathematical physics

    CERN Document Server

    Sagan, Hans

    1989-01-01

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

  6. High-order time-accurate schemes for parabolic singular perturbation problems with convection

    NARCIS (Netherlands)

    Hemker, P.W.; Shishkin, G.I.; Shishkina, L.P.

    2001-01-01

    We consider the first boundary value problem for a singularly perturbed para-bo-lic PDE with convection on an interval. For the case of sufficiently smooth data, it is easy to construct a standard finite difference operator and a piecewise uniform mesh, condensing in the boundary layer, which gives

  7. Multiple positive solutions for superlinear Kirchhoff type problems on R^N

    Directory of Open Access Journals (Sweden)

    Ghasem A. Afrouzi

    2015-12-01

    Full Text Available By using critical point theory, we establish the existence of infinitely many weak solutions for a class of Navier boundary-value problem depending on two parameters and involving the p(x-biharmonic operator. Under an appropriate oscillatory behaviour of the nonlinearity and suitable assumptions on the variable exponent, we obtain a sequence of pairwise distinct solutions.

  8. Elliptic equations in non-smooth plane domains with an application to a parabolic problem

    OpenAIRE

    Colombo, Fabrizio; Guidetti, Davide; Lorenzi, Alfredo

    2002-01-01

    In this paper we study elliptic boundary-value problems in bounded non-smooth plane domains and prove a generation result concerning analytic semigroups of linear bounded operators in space of continuous functions. Then we apply such a generation result for bounded non-smooth plane domains to a parabolic integro-differential equation.

  9. General mixed problems for the KdV equations on bounded intervals

    Directory of Open Access Journals (Sweden)

    Nikolai A. Larkin

    2010-11-01

    Full Text Available This article is concerned with initial-boundary value problems for the Korteweg-de Vries (KdV equation on bounded intervals. For general linear boundary conditions and small initial data, we prove the existence and uniqueness of global regular solutions and its exponential decay, as $toinfty$.

  10. On the solvability of Dirichlet problem for the weighted p-Laplacian

    Directory of Open Access Journals (Sweden)

    Ewa Szlachtowska

    2012-01-01

    Full Text Available The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted \\(p\\-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.

  11. GLOBAL EXISTENCE, UNIQUENESS, AND STABILITY FOR A NONLINEAR HYPERBOLIC-PARABOLIC PROBLEM IN PULSE COMBUSTION

    Institute of Scientific and Technical Information of China (English)

    Olga Terlyga; Hamid Bellout; Frederick Bloomt

    2012-01-01

    A global existence theorem is established for an initial-boundary value problem,with time-dependent boundary data,arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic system.Using results previously established for the associated linear problem,a fixed point argunent is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate a-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem.Finally,a different set of a priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original,nonlinear,hyperbolic-parabolic system.

  12. PRESSURE ASYMTOTICS IN VICINITY OF ANGULAR POINT FOR PROBLEMS OF THEORY OF PLASTICITY WITH HARDENING

    Directory of Open Access Journals (Sweden)

    V. A. Nifagin

    2015-01-01

    Full Text Available A variant of method for solution plane boundary problems of mathematical theory of plasticity  with  hardening in respect of areas containing singular boundary points is developed in the paper. Linearization of determining relationships is reached on the basis of expansion into series where the first nonlinear term is the main one. The problem is reduced to sequence of boundary-value problems for ordinary differential equations with restrictions of special type. 

  13. A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem

    OpenAIRE

    Benamou, Jean-David; Froese, Brittany D.; Oberman, Adam M.

    2012-01-01

    In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as applications in diverse areas. Numerical solution techniques for the OT problem remain underdeveloped. The solution is obtained by solving the second boundary value problem for the MA equation, a fully nonlinear elliptic partial differential equation (PDE). Instead o...

  14. All Well--Posed Problems have Uniformly Stable and Convergent Discretizations

    OpenAIRE

    Schaback, Robert

    2014-01-01

    This paper considers a large class of linear operator equations, including linear boundary value problems for partial differential equations, and treats them as linear recovery problems for objects from their data. Well-posedness of the problem means that this recovery is continuous. Discretization recovers restricted trial objects from restricted test data, and it is well-posed or stable, if this restricted recovery is continuous. After defining a general framework for these notions, this pa...

  15. Solving the Stokes problem on a massively parallel computer

    DEFF Research Database (Denmark)

    Axelsson, Owe; Barker, Vincent A.; Neytcheva, Maya; Polman, B.

    2001-01-01

    boundary value problem for each velocity component, are solved by the conjugate gradient method with a preconditioning based on the algebraic multi‐level iteration (AMLI) technique. The velocity is found from the computed pressure. The method is optimal in the sense that the computational work is...... proportional to the number of unknowns. Further, it is designed to exploit a massively parallel computer with distributed memory architecture. Numerical experiments on a Cray T3E computer illustrate the parallel performance of the method....

  16. 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.

  17. 具有边界摄动的非线性非局部反应扩散方程的奇摄动问题%The Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

    Institute of Scientific and Technical Information of China (English)

    莫嘉琪

    2006-01-01

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

  18. High-precision methods in eigenvalue problems and their applications

    CERN Document Server

    Akulenko, Leonid D

    2004-01-01

    This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems that appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics, and microelectronics.

  19. Global solutions to the two-dimensional Riemann problem for a system of conservation laws

    Science.gov (United States)

    Pang, Yicheng; Cai, Shaohong; Zhao, Yuanying

    2016-06-01

    We study the global solutions to the two-dimensional Riemann problem for a system of conservation laws. The initial data are three constant states separated by three rays emanating from the origin. Under the assumption that each ray in the initial data outside of the origin projects exactly one planar contact discontinuity, this problem is classified into five cases. By the self-similar transformation, the reduced system changes type from being elliptic near the origin to being hyperbolic far away in self-similar plane. Then in hyperbolic region, applying the generalized characteristic analysis method, a Goursat problem is solved to describe the interactions of planar contact discontinuities. While, in elliptic region, a boundary value problem arises. It is proved that this boundary value problem admits a unique solution. Based on these preparations, five explicit solutions and their corresponding criteria can be obtained in self-similar plane.

  20. Existence of a positive solution for a -Laplacian semipositone problem

    OpenAIRE

    Shivaji R; Chhetri Maya

    2005-01-01

    We consider the boundary value problem in satisfying on , where on , is a parameter, is a bounded domain in with boundary , and for . Here, is a nondecreasing function for some satisfying (semipositone). We establish a range of for which the above problem has a positive solution when satisfies certain additional conditions. We employ the method of subsuper solutions to obtain the result.