This article is cited in 1 paper

Mathematics and Mechanics

Local boundary value problems for a model equation of the third order of hyperbolic type

Zh. A. Balkizov

Institute of Applied Mathematics and Automation – branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 360000, Russia, Nalchik, 89 A Shortanov street

Abstract: Within the framework of this work, three local boundary value problems for a model equation of hyperbolic type of the third order are formulated and investigated. The solutions of the problems posed are written out explicitly. Conditions are found for given functions that ensure the regularity of solutions to the corresponding problems. The obtained representations of solutions to problems will find applications in further formulations and studies of boundary value problems for various equations of mixed and mixed-composite types with a similar model operator in the hyperbolicity domain.

Keywords: equations of hyperbolic type of the third order, characteristics of a third order equation, characteristic coordinates, local problem, nonlocal problem, general solution of the problem, regular solution of the problem.

UDC: 517.956.32

MSC: 35M12

Received: 05.09.2022
Revised: 26.09.2022
Accepted: 30.09.2022

DOI: 10.35330/1991-6639-2022-5-109-11-18

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