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 Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Issue 1, Pages 21–31 (Mi vkam230)

MATHEMATICS

The boundary value problem for the generalized moisture transfer equation

S. Kh. Gekkievaa, M. A. Kerefovb

a Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Center of RAS, 360000, Nalchik, Shortanova st., 89 A, Russia
b Kabardino-Balkarian State University named after H. M. Berbekov, 360004, Nalchik, Chernyshevsky st., 173, Russia

Abstract: In mathematical modeling of continuous media with memory, we deal with equations that describe a new type of wave motion, something between ordinary wave diffusion and classical wave propagation. There are fractional differential equations, which are the basis for the most mathematical models describing a wide class of physical and chemical processes in the fractal geometry of the Nature. The paper presents a new moisture transfer equation with a fractional Riemann–Liouville derivative that generalize the Aller–Lykov equation. The first boundary value problem for the generalized moisture transfer equation is considered. To prove the uniqueness of a solution we employ the energy inequalities method; an a priori estimate is obtained in terms of the fractional Riemann–Liouville derivative. The existence of the solution for the problem is proved by the Fourier method.

Keywords: Tricomi problem, parabolic-hyperbolic equation, non-characteristic plane, Fourier transform, maximum principle, apriori estimate, uniqueness, existence, system of integral equations.

DOI: https://doi.org/10.18454/2079-6641-2018-21-1-21-31

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Document Type: Article
UDC: 517.95
MSC: 35E99

Citation: S. Kh. Gekkieva, M. A. Kerefov, “The boundary value problem for the generalized moisture transfer equation”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 1, 21–31

Citation in format AMSBIB
\Bibitem{GekKer18} \by S.~Kh.~Gekkieva, M.~A.~Kerefov \paper The boundary value problem for the generalized moisture transfer equation \jour Vestnik KRAUNC. Fiz.-Mat. Nauki \yr 2018 \issue 1 \pages 21--31 \mathnet{http://mi.mathnet.ru/vkam230} \crossref{https://doi.org/10.18454/2079-6641-2018-21-1-21-31} \elib{http://elibrary.ru/item.asp?id=32833882}