Geodesic
Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 112-116

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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
Mots-clés : fractional diffusion equation, transport equation. 
@article{INTO_2019_167_a9,
     author = {K. U. Khubiev},
     title = {Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {112--116},
     publisher = {mathdoc},
     volume = {167},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_167_a9/}
}
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K. U. Khubiev. Boundary-value problem for a loaded hyperbolic-parabolic equation with degeneration of order. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 112-116. http://geodesic.mathdoc.fr/item/INTO_2019_167_a9/