Geodesic
Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 127-138

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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. 
@article{INTO_2021_195_a14,
     author = {K. U. Khubiev},
     title = {Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {127--138},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a14/}
}
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K. U. Khubiev. Boundary-value problems for a characteristically loaded hyperbolic-parabolic equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 127-138. http://geodesic.mathdoc.fr/item/INTO_2021_195_a14/