This article is cited in 2 papers

MATHEMATICS

Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation

Zh. A. Balkizov

Institute of Applied Mathematics and Automation, Nalchik

Abstract: In this paper, we study a nonlocal problem with a shift to conjugation of two equations of second-order hyperbolic type, consisting of a wave equation in one part of the domain and a degenerate hyperbolic equation of the first kind in the other part. Using the Tricomi method, sufficient conditions arc found for given functions that ensure the existence of a unique solution of the problem under study that is regular in the region under consideration. In a particular case, the solution of the problem is written out explicitly.

Keywords: In this paper, we study a nonlocal problem with a shift to conjugation of two equations of second-order hyperbolic type, consisting of a wave equation in one part of the domain and a degenerate hyperbolic equation of the first kind in the other part. Using the Tricomi method, sufficient conditions arc found for given functions that ensure the existence of a unique solution of the problem under study that is regular in the region under consideration. In a particular case, the solution of the problem is written out explicitly.

UDC: 517.956.32

Received: 17.03.2023
Revised: 21.03.2023
Accepted: 23.03.2023

DOI: 10.47928/1726-9946-2023-23-1-11-19

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