半约束平面域中同质抛物系统的初始边界问题及互补条件

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2024-02-26 DOI:10.1134/s0012266123120066

S. I. Sakharov

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引用次数: 0

摘要

摘要我们考虑了在具有非光滑横向边界的半约束平面域中，初始条件为零且系数满足双 Dini 条件的均质抛物系统的初始边界值问题。利用边界积分方程的方法，证明了此类问题在函数空间中的唯一经典可解性定理，这些函数与其在域闭合中的第一次空间导数是连续的。给出了所得解的积分表示。结果表明，本文所考虑的问题的可解性条件等同于众所周知的互补性条件。

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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Initial–Boundary Value Problems for Homogeneous Parabolic Systems in a Semibounded Plane Domain and Complementarity Condition

Abstract

We consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with zero initial conditions in a semibounded plane domain with nonsmooth lateral boundary. The method of boundary integral equations is used to prove a theorem on the unique classical solvability of such problems in the space of functions that are continuous together with their first spatial derivative in the closure of the domain. An integral representation of the obtained solutions is given. It is shown that the condition for the solvability of the posed problems considered in the paper is equivalent to the well-known complementarity condition.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.