Abstract:
In this paper, we study the nonlocal Bitsadze–Samarskii-type problem with internal boundary conditions for a loaded hyperbolic-parabolic equation with order degeneracy in the hyperbolicity domain. These boundary conditions are a special case of Nakhushev's nonlocal condition. We find the condition for existence and uniqueness of a solution to the problem and obtain a representation of the solution in the parabolic part of the domain and the explicit solution in the hyperbolic part of the domain.
Citation:
K. U. Khubiev, “The Bitsadze–Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 198, VINITI, Moscow, 2021, 123–132
\Bibitem{Khu21}
\by K.~U.~Khubiev
\paper The Bitsadze--Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 198
\pages 123--132
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into882}
\crossref{https://doi.org/10.36535/0233-6723-2021-198-123-132}
Citation in format AMSBIB
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