Initial-Boundary Value Problems for Parabolic Systems in a Semibounded Plane Domain with General Boundary Conditions
Pub Date : 2024-07-18
DOI:10.1134/s0965542524700507
引用次数: 0
Abstract
Initial-boundary value problems are considered for homogeneous parabolic systems with Dini-continuous coefficients and zero initial conditions in a semibounded plane domain with a nonsmooth lateral boundary admitting cusps, on which general boundary conditions with variable coefficients are given. A theorem on unique classical solvability of these problems in the space of functions that are continuous and bounded together with their first spatial derivatives in the closure of the domain is proved by applying the boundary integral equation method. A representation of the resulting solutions in the form of vector single-layer potentials is given.
具有一般边界条件的半约束平面域中抛物系统的初边界问题
摘要 本文考虑了在半边界平面域中具有迪尼连续系数和零初始条件的同质抛物线系统的初始边界值问题，该平面域具有非光滑的横向边界，允许尖角，在该边界上给出了具有可变系数的一般边界条件。通过应用边界积分方程方法，证明了这些问题在函数空间中的唯一经典可解性定理，这些函数在域的闭合中是连续的、有界的，并带有它们的第一个空间导数。还给出了以矢量单层势的形式表示所得到的解的方法。
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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