This article is cited in 14 papers

MATHEMATICS

Uniqueness of solutions of initial-boundary value problems for parabolic systems with Dini-continuous coefficients in domains on the plane

E. A. Baderko, S. I. Saharov

Lomonosov Moscow State University, Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

Abstract: The first and second initial-boundary value problems for Petrovskii parabolic systems of the second order with coefficients satisfying the Dini condition in plane domains with nonsmooth lateral boundaries admitting, in particular, cusps are considered. Theorems on the uniqueness of classical solutions of these problems in the class of functions that are continuous and bounded together with their first spatial derivatives in the closure of these domains are proved.

Keywords: parabolic system, initial-boundary value problem, uniqueness of a classical solution, nonsmooth lateral boundary, boundary integral equations.

UDC: 517.956.4

Presented: E. I. Moiseev
Received: 19.01.2022
Revised: 19.01.2022
Accepted: 22.01.2022

DOI: 10.31857/S2686954322020060

 English version: Doklady Mathematics, 2022, 105:2, 71–74

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