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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 167, Pages 112–116 (Mi into492)  

Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order

K. U. Khubiev

Institute of Applied Mathematics and Automation, Nalchik

Abstract: In this paper, we study a boundary-value problem with discontinuous conjugation conditions on the line of type changing for a model equation of mixed hyperbolic-parabolic type with order degeneration in the hyperbolicity domain. In the parabolic domain, the equation is the fractional diffusion equation, whereas in the hyperbolic domain it is the loaded one-speed transport equation. We prove the uniqueness and existence theorem and propose an explicit solution of the problem in the parabolic and hyperbolic domains.

Keywords: boundary-value problem, loaded equation, mixed-type equation, hyperbolic-parabolic equation, fractional diffusion equation, transport equation

DOI: https://doi.org/10.36535/0233-6723-2019-167-112-116

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UDC: 517.95
MSC: 35M10, 35M12

Citation: K. U. Khubiev, “Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 167, VINITI, Moscow, 2019, 112–116

Citation in format AMSBIB
\Bibitem{Khu19}
\by K.~U.~Khubiev
\paper Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22Ц26, 2018. Part III
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 167
\pages 112--116
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into492}
\crossref{https://doi.org/10.36535/0233-6723-2019-167-112-116}
\elib{https://elibrary.ru/item.asp?id=42319657}


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