共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we consider the boundary value problem with the shift for nonlinear uniformly elliptic equations of second order in a multiply connected domain. For this sake, we propose a modified boundary value problem for nonlinear elliptic systems of first order equations, and give a priori estimates of solutions for the modified boundary value problem. Afterwards we prove by using the Schauder fixedpoint theorem that this boundary value problem with some conditions has a solution. The result obtained is the generlization of the corresponding theorem on the Poincare boundary value problem. 相似文献
2.
I. V. Volovich V. Zh. Sakbaev 《Proceedings of the Steklov Institute of Mathematics》2014,285(1):56-80
A new statement of a boundary value problem for partial differential equations is discussed. An arbitrary solution to a linear elliptic, hyperbolic, or parabolic second-order differential equation is considered in a given domain of Euclidean space without any constraints imposed on the boundary values of the solution or its derivatives. The following question is studied: What conditions should hold for the boundary values of a function and its normal derivative if this function is a solution to the linear differential equation under consideration? A linear integral equation is defined for the boundary values of a solution and its normal derivative; this equation is called a universal boundary value equation. A universal boundary value problem is a linear differential equation together with a universal boundary value equation. In this paper, the universal boundary value problem is studied for equations of mathematical physics such as the Laplace equation, wave equation, and heat equation. Applications of the analysis of the universal boundary value problem to problems of cosmology and quantum mechanics are pointed out. 相似文献
3.
Zuo-liang Xu 《应用数学学报(英文版)》2007,23(4):629-636
In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed. 相似文献
4.
The mixed boundary value problem is considered for an anisotropic elastic body under the condition that a boundary value of the displacement vector is given on some part of the boundary and a boundary value of the generalized stress vector on the remainder. Using the potential method and the theory of singular integral equations with discontinuous coefficients, the existence of a solution of the mixed boundary value problem is proved. 相似文献
5.
A free boundary value problem is introduced to approximate the original Thomas–Fermi equation. The unknown truncated free
boundary is determined iteratively. We transform the free boundary value problem to a nonlinear boundary value problem defined
on [0,1]. We present an adaptive algorithm to solve the problem by means of the moving mesh finite element method. Comparison
of our numerical results with those obtained by other approaches shows high accuracy of our method. 相似文献
6.
In this article, Haseman boundary value problem for a class of meta-analytic functions is studied. The expression of solution and the condition of solvability for Haseman boundary value problem are obtained by changing the problem discussed into the equivalent Haseman boundary value problem of bi-analytic function. And the expression of solution and the condition of solvability depend on the canonical matrix. 相似文献
7.
Heinz Fiedler 《manuscripta mathematica》1972,7(2):185-196
In this note we derive a necessary requirement for the self-adjointness of a boundary value problem of ordinary differential equations, which involves only the leading coefficients of the normalized boundary conditions. As application it is shown that every self-adjoint boundary value problem of even order (and thus especially every real self-adjoint boundary value problem) is regular. The proof of this fact depends on the evaluation of a sort of generalized Vandermonde's determinant. 相似文献
8.
本文研究带有抽取的非饱和流动中出现的一个非线性边值问题.利用互惠变换及HopfCole变换将问题化为一个移动边界问题,进而获得了Fourier级数解. 相似文献
9.
A. I. Korotkii Yu. V. Starodubtseva 《Proceedings of the Steklov Institute of Mathematics》2015,291(1):96-112
Direct and inverse boundary value problems for models of stationary reaction–convection–diffusion are investigated. The direct problem consists in finding a solution of the corresponding boundary value problem for given data on the boundary of the domain of the independent variable. The peculiarity of the direct problem consists in the inhomogeneity and irregularity of mixed boundary data. Solvability and stability conditions are specified for the direct problem. The inverse boundary value problem consists in finding some traces of the solution of the corresponding boundary value problem for given standard and additional data on a certain part of the boundary of the domain of the independent variable. The peculiarity of the inverse problem consists in its ill-posedness. Regularizing methods and solution algorithms are developed for the inverse problem. 相似文献
10.
应用算子特征值准则研究了一类高阶多点边值问题多重正解的存在性,其中非线性项满足Caratheodory条件.将特征值准则应用到n阶m点的非线性边值问题,并证明了微分方程至少三正解的存在性. 相似文献
11.
We consider a boundary value problem generated by the Sturm-Liouville equation on a finite interval. Both the equation and the boundary conditions depend quadratically on the spectral parameter. This boundary value problem occurs in the theory of small vibrations of a damped string. The inverse problem, i.e., the problem of recovering the equation and the boundary conditions from the given spectrum, is solved. 相似文献
12.
《高校应用数学学报(英文版)》2016,(4)
Firstly, the Riemann boundary value problem for a kind of degenerate elliptic system of the first order equations in R~4 is proposed. Then, with the help of the one-to-one correspondence between the theory of Clifford valued generalized regular functions and that of the degenerate elliptic system's solution, the boundary value problem as stated above is transformed into a boundary value problem related to the generalized regular functions in Clifford analysis. Moreover, the solution of the Riemann boundary value problem for the degenerate elliptic system is explicitly described by using a kind of singular integral operator. Finally, the conditions for the existence of solutions of the oblique derivative problem for another kind of degenerate elliptic system of the first order equations in R~4 are derived. 相似文献
13.
《Journal of Computational and Applied Mathematics》1987,17(3):345-354
This paper deals with the application of a variational method to a boundary value problem of the wave equation. Starting with an initial boundary value problem (which is given) introduction of a boundary condition at the final time leads to a boundary value problem with one of the initial conditions redundant. This redundant initial condition is used by the trial function of the direct method (of the Ritz type) which is employed to stationarize the variational principle. 相似文献
14.
讨论推广的海底取油管振动方程的初边值问题和初值问题解的整体不存在性,对初边值问题推广了Gmira和Guedda得到的结果,对初值问题的结果是新的. 相似文献
15.
We consider a boundary value problem for the Laplace operator in a model domain periodically perforated along the boundary.
We assume that the homogeneous Neumann condition is posed on the exterior boundary and the homogeneous Dirichlet condition
is posed on the boundary of the cavities. We construct and justify the asymptotic expansions of eigenelements of the boundary
value problem. 相似文献
16.
本文研究了一般周期Riemann边值问题关于跳跃曲线的稳定性.利用解析函数边值理论和不等式分析理论,获得了一般周期Riemann边值问题的解及其关于跳跃曲线的误差估计. 相似文献
17.
Fazhan Geng 《Applied mathematics and computation》2011,218(8):4211-4215
In this paper, a novel method is presented for solving a class of singularly perturbed boundary value problems. Firstly the original problem is reformulated as a new boundary value problem whose solution does not change rapidly via a proper transformation; then the reproducing kernel method is employed to solve the boundary value new problem. Numerical results show that the present method can provide very accurate analytical approximate solutions. 相似文献
18.
非凸单个守恒律初边值问题的整体弱熵解的构造 总被引:4,自引:0,他引:4
本文研究具有两段常数的初始值和常数边界值的非凸单个守恒律的初边值问题.在流函数具有一个拐点的条件下,由相应的初始值问题弱熵解的结构和Bardos-Leroux-Nedelec提出的边界熵条件,给出初边值问题整体弱熵解的一个构造方法,澄清弱熵解在边界附近的结构.与严格凸的单个守恒律初边值问题相比,非凸单个守恒律初边值问题的弱熵解中包括下列新的相互作用类型:一个接触或非接触激波碰到边界,边界弹回一个非接触激波. 相似文献
19.
Construction of Solutions and L^1-error Estimates of Viscous Methods for Scalar Conservation Laws with Boundary 总被引:4,自引:0,他引:4
Hong Xia LIU Tao PAN 《数学学报(英文版)》2007,23(3):393-410
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O(ε^1/2) in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O(ε| In ε|). 相似文献
20.
Yu. N. Kiselev M. V. Orlov S. M. Orlov 《Moscow University Computational Mathematics and Cybernetics》2018,42(4):152-162
The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest. 相似文献