Adyghe Int. Sci. J. Vol. 23. No 1. P. 11-19
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DOI: https://doi.org/10.47928/1726-9946-2023-23-1-11-19
EDN: ACKBLJ
MATHEMATICS
| MSC 35М12 | Original Article |
Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation
Zhiraslan Anatolevich Balkizov
Ph.D. (Phys & Math) Leading Researcher, Department of Mixed Type Equations, Institute of Applied Mathematics and Automation of KBSC RAS, (360017, 89 A Shortanova St., Nalchik, Russia), https://orcid.Org/0000-0001-5329-7766, Giraslan@yandcx.ru
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: wave equation, degenerate hyperbolic equation, Volterra equation, Tricomi method, method of integral equations, methods of the theory of fractional calculus
Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.
For citation. Balkizov G. A. Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation. Adyghe hit. Sei. J. 2023. Vol. 23, No. 1. P. 11-19.
DOI: https://doi.org/10.47928/1726-9946-2023-23-1-11-19; EDN: ACKBLJ
The author has read and approved the final version of the manuscript.
Submitted 13.12.2022; approved after reviewing 21.12.2022; accepted for publication 24.12.2022
© Balkizov G. A., 2023
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