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Abstract <p> The first initial–boundary value problem for a Petrovskii parabolic second-order system ina bounded domain on the plane is investigated. The coefficients of the system satisfy the doubleDini condition. The lateral boundaries of the domain admit cusps at the initial time. Theexistence of a solution of this problem in the space of functions continuous together with theirhigher-order derivatives in the closure of the domain is studied. An integral representation of thesolution is obtained, and the corresponding estimates are established.</p>

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On the Solvability of the First Initial–Boundary Value Problem for Parabolic Systems in a Bounded Domain with Nonsmooth Lateral Boundaries on the Plane

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • K. D. Fedorov

摘要

Abstract

The first initial–boundary value problem for a Petrovskii parabolic second-order system ina bounded domain on the plane is investigated. The coefficients of the system satisfy the doubleDini condition. The lateral boundaries of the domain admit cusps at the initial time. Theexistence of a solution of this problem in the space of functions continuous together with theirhigher-order derivatives in the closure of the domain is studied. An integral representation of thesolution is obtained, and the corresponding estimates are established.