Bitsadze-Samarsky type problems with double involution

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-07-09 DOI:10.1186/s13661-024-01892-w

Moldir Muratbekova, Valery Karachik, Batirkhan Turmetov

引用次数: 0

Abstract

In this paper, the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. Nonlocal conditions are specified in the form of a connection between the values of the unknown function at different points of the boundary. In this case, the boundary operator is determined using matrices of involution-type mappings. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Using Green’s functions of the classical Dirichlet and Neumann boundary value problems, Green’s functions of the studied problems are constructed and integral representations of solutions to these problems are obtained.

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带双卷积的比萨泽-萨马尔斯基类型问题

本文研究了泊松方程的一类新的非局部边界值问题的可解性。非局部条件是以未知函数在边界不同点的值之间的联系形式指定的。在这种情况下，边界算子是利用反卷型映射矩阵确定的。我们证明了所研究问题的解的存在性和唯一性定理。利用经典 Dirichlet 和 Neumann 边界值问题的格林函数，构建了所研究问题的格林函数，并获得了这些问题解的积分表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.