Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Issue 1(21), Pages 21–31
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
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.
Tricomi problem, parabolic-hyperbolic equation, non-characteristic plane, Fourier transform, maximum principle, apriori estimate, uniqueness, existence, system of integral equations.
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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), 21–31
Citation in format AMSBIB
\by S.~Kh.~Gekkieva, M.~A.~Kerefov
\paper The boundary value problem for the generalized moisture transfer equation
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
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