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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2018, Volume 24, Issue 3, Pages 23–29 (Mi vsgu579)

Mathematics

Boundary value problem for the Aller–Lykov moisture transport generalized equation with concentrated heat capacity

M. A. Kerefova, F. M. Nakhushevaa, S. Kh. Gekkievab

a Department of Applied Mathematics and Informatics, Kabardino-Balkarian State University named after H.M. Berbekov, 173, Chernyshevsky Street, Nalchik, 360004, Russian Federation
b Department of Mathematical Modeling of Geophysical Processes, Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2, Balkarova Street, Dolinsk, Nalchik, 360002, Russian Federation

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.

Keywords: Aller's–Lykov equation, fractional derivative, nonlocal problem, moisture transfer generalized equation, concentrated heat capacity, inequalities method, a priori estimate, boundary value problem.

DOI: https://doi.org/10.18287/2541-7525-2018-24-3-23-29

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UDC: 517.95

Citation: M. A. Kerefov, F. M. Nakhusheva, S. Kh. Gekkieva, “Boundary value problem for the Aller–Lykov moisture transport generalized equation with concentrated heat capacity”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:3 (2018), 23–29

Citation in format AMSBIB
\Bibitem{KerNakGek18} \by M.~A.~Kerefov, F.~M.~Nakhusheva, S.~Kh.~Gekkieva \paper Boundary value problem for the Aller--Lykov moisture transport generalized equation with concentrated heat capacity \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2018 \vol 24 \issue 3 \pages 23--29 \mathnet{http://mi.mathnet.ru/vsgu579} \crossref{https://doi.org/10.18287/2541-7525-2018-24-3-23-29} \elib{https://elibrary.ru/item.asp?id=36731739}