The Bitsadze--Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 123-132
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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.
Keywords:
loaded equation, mixed-type equation, hyperbolic-parabolic equation, nonlocal problem, Bitsadze—Samarskii problem, Nakhushev's nonlocal condition.
@article{INTO_2021_198_a13,
author = {K. U. Khubiev},
title = {The {Bitsadze--Samarskii} problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain},
journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
pages = {123--132},
publisher = {mathdoc},
volume = {198},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a13/}
}
TY - JOUR AU - K. U. Khubiev TI - The Bitsadze--Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2021 SP - 123 EP - 132 VL - 198 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2021_198_a13/ LA - ru ID - INTO_2021_198_a13 ER -
%0 Journal Article %A K. U. Khubiev %T The Bitsadze--Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2021 %P 123-132 %V 198 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2021_198_a13/ %G ru %F INTO_2021_198_a13
K. U. Khubiev. The Bitsadze--Samarskii problem for a loaded hyperbolic-parabolic equation with degeneracy of order in the hyperbolicity domain. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 123-132. http://geodesic.mathdoc.fr/item/INTO_2021_198_a13/