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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2021, Volume 195, Pages 127–138 (Mi into841)  

Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation

K. U. Khubiev

Institute of Applied Mathematics and Automation, Nalchik

Abstract: In this paper, we consider analogs of the Tricomi problem, problems with displacement, and problems with integral conditions in the hyperbolic part for a certain characteristically loaded model equation of mixed hyperbolic-parabolic type. We find sufficient conditions of the existence of a unique solution. The uniqueness and existence of a solution are proved by the Tricomi method and the method of integral equations, respectively. We give an example, which shows that the violation of these conditions leads to nonuniqueness of the solution.

Keywords: loaded equation, mixed-type equation, hyperbolic-parabolic equation, Tricomi problem, nonlocal problem, problem with displacement, integral condition

DOI: https://doi.org/10.36535/0233-6723-2021-195-127-138

Full text: PDF file (181 kB)
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UDC: 517.95
MSC: 35M10, 35M12

Citation: K. U. Khubiev, “Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation”, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 195, VINITI, Moscow, 2021, 127–138

Citation in format AMSBIB
\Bibitem{Khu21}
\by K.~U.~Khubiev
\paper Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation
\inbook Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 195
\pages 127--138
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into841}
\crossref{https://doi.org/10.36535/0233-6723-2021-195-127-138}


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