Geodesic
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/}
}
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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/