BOUNDARY VALUE PROBLEM FOR THE ALLER — LYKOV MOISTURE TRANSPORT GENERALIZED EQUATION WITH CONCENTRATED HEAT CAPACITY


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Abstract

The article considers the Aller — Lykov equation with a Riemann — Liouville fractional time derivative, boundary conditions of the third kind and with the concentrated specific heat capacity on the boundary of the domain. Similar conditions arise in the case with a material of a higher thermal conductivity when solving a temperature problem for restricted environment with a heater as a concentrated heat capacity. Analogous conditions also arise in practices for regulating the water-salt regime of soils, when desalination of the upper layer is achieved by draining of a surface of the flooded for a while area. Using energy inequality methods, we obtained an a priori estimate in terms of the Riemann — Liouville fractional derivative, which revealed the uniqueness of the solution to the problem under consideration.

About the authors

M. A. Kerefov

Kabardino-Balkarian State University named after H.M. Berbekov

Author for correspondence.
Email: morenov@ssau.ru

F. M. Nakhusheva

Kabardino-Balkarian State University named after H.M. Berbekov

Email: morenov@ssau.ru

S. Kh. Gekkieva

Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences

Email: morenov@ssau.ru

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Copyright (c) 2019 М. А. Керефов, Ф. М. Нахушева, С. Х. Геккиева

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