共查询到20条相似文献,搜索用时 46 毫秒
1.
I. S. Mokrousov 《Differential Equations》2017,53(4):509-515
We consider four mixed problems for the string vibration equation with zero initial conditions, with a Bitsadze–Samarskii boundary condition of the general form at the right endpoint, and with an inhomogeneous Neumann or Dirichlet condition at the left endpoint. We prove the uniqueness of a generalized solution (in the sense of Il’in) of these problems and obtain an analytic representation of these solutions. The solution of each of the problems is represented in the form of a linear combination of functions constructed from the problem data, and recursion formulas for the coefficients of this linear combination are obtained. 相似文献
2.
A. P. Soldatov 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):233-240
The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent’ev-Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze’s terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex. 相似文献
3.
一类Dirichlet边值逆问题 总被引:2,自引:0,他引:2
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. 相似文献
4.
On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions
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Mokhtar Kirane Berikbol T. Torebek 《Mathematical Methods in the Applied Sciences》2016,39(5):1121-1128
In this paper, we investigate the correct solvability for the Laplace equation with a nonlocal boundary condition in the unit ball. The considered boundary operator is of fractional order. This problem is a generalization of the well‐known Bitsadze–Samarskii problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
Linear and nonlinear elliptic complex partial differential equations of higher‐order are considered under Schwarz conditions in the upper‐half plane. Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schwarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro‐differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively. 相似文献
6.
A Dirichlet problem for polyharmonic functions 总被引:1,自引:0,他引:1
In this article, the Dirichlet problem of polyharmonic functions is considered. As well the explicit expression of the unique
solution to the simple Dirichlet problem for polyharmonic functions is obtained by using the decomposition of polyharmonic
functions and turning the problem into an equivalent Riemann boundary value problem for polyanalytic functions, as the approach
to find the kernel functions of the solution for the general Dirichlet problem is given.
Project supported by NNSF of China. 相似文献
7.
H. M. Hayrapetyan A. R. Hayrapetyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2012,47(1):1-15
The paper investigates the Schwarz type boundary value problem for polyanalytic functions when the boundary functions belong
to weighted space L
1(ρ). 相似文献
8.
A. R. Bikmetov 《Computational Mathematics and Mathematical Physics》2006,46(4):636-650
Asymptotics of eigenelements of a singularly perturbed boundary value problem for the three-dimensional Schrödinger operator is constructed in a bounded domain with the Dirichlet and Neumann boundary condition. The perturbation is described by a large potential whose support contracts into a point. In the case of the Dirichlet boundary conditions, this problem corresponds to a potential well with infinitely high walls and a narrow finite peak at the bottom. 相似文献
9.
In this article we give the solvability conditions and an integral representation of the solution of a Robin problem for the Bitsadze equation in the upper half plane. In order to do that, we use classical results of complex analysis and carry out the composition of two Robin problems for the Cauchy Riemann operator. 相似文献
10.
We consider a singularly perturbed boundary-value eigenvalue problem for the Laplace operator in a cylinder with rapidly alternating type of the boundary condition on the lateral surface. The change of the boundary conditions is realized by splitting the lateral surface into many narrow strips on which the Dirichlet and Neumann conditions alternate. We study the case in which the averaged problem contains the Dirichlet boundary condition on the lateral surface. In the case of strips with slowly varying width we construct the first terms of the asymptotic expansions of eigenfunctions; moreover, in the case of strips with rapidly varying width we obtain estimates for the convergence rate. 相似文献
11.
A. G. Chechkina 《Journal of Mathematical Sciences》2009,162(3):443-458
We consider boundary value problems for the Laplace operator in a domain with boundary conditions of rapidly varying type:
the Dirichlet homogeneous condition and the third (Fourier) boundary condition or a Steklov type condition. We construct the
limit (homogenized) problem and prove that solutions, eigenvalues, and eigenfunctions of the original problem converge respectively
to solutions, eigenvalues, and eigenfunctions of the limit problem. Bibliography: 47 titles. Illustrations: 2 figures. 相似文献
12.
D. B. Davletov 《Computational Mathematics and Mathematical Physics》2008,48(10):1811-1822
A boundary value problem for the Lame operator in a bounded three-dimensional domain with a small cavity is studied. The domain is filled with an elastic homogeneous isotropic medium that is clamped at the boundary, which corresponds to the Dirichlet boundary condition. The leading term of an asymptotic expansion for the eigenvalue is constructed in the case of the Dirichlet limit problem. The asymptotic expansion is constructed in powers of a small parameter ? that is the diameter of the cavity. 相似文献
13.
The Cauchy kernel is one of the two significant tools for solving the Riemann boundary value problem for analytic functions. For poly-domains, the Cauchy kernel is modified in such a way that it corresponds to a certain symmetry of the boundary values of holomorphic functions in poly-domains. This symmetry is lost if the classical counterpart of the one-dimensional form of the Cauchy kernel is applied. It is also decisive for the establishment of connection between the Riemann–Hilbert problem and the Riemann problem. Thus, not only the Schwarz problem for holomorphic functions in poly-domains is solved, but also the basis is established for solving some other problems. The boundary values of functions, holomorphic in poly-domains, are classified in the Wiener algebra. The general integral representation formulas for these functions, the solvability conditions and the solutions of the corresponding Schwarz problems are given explicitly. A necessary and sufficient condition for the boundary values of a holomorphic function for arbitrary poly-domains is given. At the end, well-posed formulations of the torus-related problems are considered. 相似文献
14.
We consider a planar waveguide modeled by the Laplacian in a straight infinite strip with the Dirichlet boundary condition
on the upper boundary and with frequently alternating boundary conditions (Dirichlet and Neumann) on the lower boundary. The
homogenized operator is the Laplacian subject to the Dirichlet boundary condition on the upper boundary and to the Dirichlet
or Neumann condition on the lower one. We prove the uniform resolvent convergence for the perturbed operator in both cases
and obtain the estimates for the rate of convergence. Moreover, we construct the leading terms of the asymptotic expansions
for the first band functions and the complete asymptotic expansion for the bottom of the spectrum. Bibliography: 17 titles.
Illustrations: 3 figures. 相似文献
15.
R. R. Gadyl’shin S. V. Rep’evskii E. A. Shishkina 《Proceedings of the Steklov Institute of Mathematics》2016,292(1):76-90
A boundary-value problem of finding eigenvalues is considered for the negative Laplace operator in a disk with Neumann boundary condition on almost all the circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. A complete asymptotic expansion with respect to a parameter (the length of the small arc) is constructed for an eigenvalue of this problem that converges to a double eigenvalue of the Neumann problem. 相似文献
16.
Ricardo Abreu Blaya Lianet De la Cruz Toranzo 《Journal of Mathematical Analysis and Applications》2021,493(2):124559
This paper is concerned with the problem of decomposing a higher order Lipschitz function on a closed Jordan curve Γ into a sum of two polyanalytic functions in each open domain defined by Γ. Our basic tools are the Hardy projections related to a singular integral operator arising in polyanalytic function theory, which, as it is proved here, represents an involution operator on the higher order Lipschitz classes. Our result generalizes the classical Hardy decomposition of Hölder continuous functions on the boundary of a domain. 相似文献
17.
Doklady Mathematics - We consider a quasilinear parabolic boundary value problem with a nonlocal boundary condition of Bitsadze–Samarskii type. A theorem on the existence and uniqueness of a... 相似文献
18.
Summary. We study the additive and multiplicative Schwarz domain decomposition methods for elliptic boundary value problem of order
2 r based on an appropriate spline space of smoothness . The finite element method reduces an elliptic boundary value problem to a linear system of equations. It is well known that
as the number of triangles in the underlying triangulation is increased, which is indispensable for increasing the accuracy
of the approximate solution, the size and condition number of the linear system increases. The Schwarz domain decomposition
methods will enable us to break the linear system into several linear subsystems of smaller size. We shall show in this paper
that the approximate solutions from the multiplicative Schwarz domain decomposition method converge to the exact solution
of the linear system geometrically. We also show that the additive Schwarz domain decomposition method yields a preconditioner
for the preconditioned conjugate gradient method. We tested these methods for the biharmonic equation with Dirichlet boundary
condition over an arbitrary polygonal domain using cubic spline functions over a quadrangulation of the given domain. The computer experiments agree with our theoretical results.
Received December 28, 1995 / Revised version received November 17, 1998 / Published online September 24, 1999 相似文献
19.
J. Giroire T. Ha‐Duong V. Moumas 《Mathematical Methods in the Applied Sciences》2005,28(13):1527-1552
This article deals with a boundary value problem for Laplace equation with a non‐linear and non‐local boundary condition. This problem comes from petroleum engineering and is used to obtain an estimation of well productivity. The non‐linear and non‐local boundary condition is written on the well boundary. On the outer reservoir boundaries, we have both Dirichlet and Neumann conditions. In this paper, we prove the existence and uniqueness of a solution to this problem. The existence is proved by Schauder theorem and the uniqueness is obtained under more restricted conditions, when the involved operator is a contraction. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
20.
A boundary value problem for the Helmholtz equation outside an open arc in a plane is studied with mixed boundary conditions. In doing so, the Dirichlet condition is specified on one side of the open arc and the boundary condition of the third kind is specified on the other side of the open arc. We consider non-propagative Helmholtz equation, real-valued solutions of which satisfy maximum principle. By using the potential theory the boundary value problem is reduced to a system of singular integral equations with additional conditions. By regularization and subsequent transformations, this system is reduced to a vector Fredholm equation of the second kind and index zero. It is proved that the obtained vector Fredholm equation is uniquely solvable. Therefore the integral representation for a solution of the original boundary value problem is obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献