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Abstract <p> An initial–boundary value problem is considered for an inhomogeneous parabolic systemwith Dini-continuous coefficients with a nonzero initial condition in a plane bounded domain withnonsmooth lateral boundaries allowing the presence of “cusps” on which general boundaryconditions are given for the components of the sought vector function. Theorems on the existenceand uniqueness of the classical solution to the problem from the space of vector functions that arecontinuous with their spatial derivatives of the first order in the closure of the domain are proved.An integral representation is given, and the smoothness of the obtained solution is investigated.</p>

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On the Unique Solvability of Initial–Boundary Value Problems for Parabolic Systems in a Plane Bounded Domain with General Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • S. I. Sakharov

摘要

Abstract

An initial–boundary value problem is considered for an inhomogeneous parabolic systemwith Dini-continuous coefficients with a nonzero initial condition in a plane bounded domain withnonsmooth lateral boundaries allowing the presence of “cusps” on which general boundaryconditions are given for the components of the sought vector function. Theorems on the existenceand uniqueness of the classical solution to the problem from the space of vector functions that arecontinuous with their spatial derivatives of the first order in the closure of the domain are proved.An integral representation is given, and the smoothness of the obtained solution is investigated.