This article is cited in 3 papers

MATHEMATICS

Classical solutions of the first boundary value problem for parabolic systems on the plane

A. N. Konenkov

Ryazan State University S. A. Esenin, Ryazan, Russia

Abstract: The first boundary value problem for a second-order parabolic system with one spatial variable in a domain with nonsmooth lateral boundaries is considered. The domain can be bounded or semi-bounded. The coefficients of the system depend only on the spatial variable and satisfy the Hölder condition. The initial and boundary functions are assumed to be continuous and bounded. The existence and uniqueness of a classical solution of this problem is established.

Keywords: parabolic system, first boundary value problem, nonsmooth lateral boundary, classical solution.

UDC: 517.956.4

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

DOI: 10.31857/S2686954322020138

 English version: Doklady Mathematics, 2022, 105:2, 109–111

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