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Vol. 24, No. 2. P. 16–26

Adyghe Int. Sci. J. Vol. 24, No. 2. Pp. 16–26. 

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DOI: https://doi.org/10.47928/1726-9946-2024-24-2-16-26
EDN: PGELNG

MATHEMATICS

UDK 517.956.32

MSC 35М12

 Original Article

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

Giraslan 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@yandex.ru

Abstract. The paper investigates a nonlocal problem with a shift to the conjugation of model equations of parabolic and hyperbolic types of the second order, consisting of a heat equation in the parabolic part of the mixed domain and a degenerate hyperbolic equation of the first kind in the other part. Using an analogue of the Tricomi method and known properties of the theory of fractional calculus, sufficient conditions for given functions are found to ensure the existence of a unique solution to the problem under study that is regular in the domain under consideration. In one particular case, the solution to the problem is written out explicitly.

Keywords: mixed type equation, heat equation, degenerate hyperbolic equation, fractional calculus, Volterra equation, Tricomi method, method of integral equations.

Funding. The work was not carried out within the framework of funds.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for submitting the final version of the article to the press.

For citation. Balkizov G. A. Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation. Adyghe Int. Sci. J. 2024. Vol. 24, No. 2. Pp. 16–26. DOI: https://doi.org/10.47928/1726-9946-2024-24-2-16-26; EDN: PGELNG

Submitted 20.06.2024; approved after reviewing 24.06.2024; aeeepted for publication 25.06.2024.

© Balkizov G. A., 2024

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