Geodesic
The boundary value problem for the generalized moisture transfer equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2018), pp. 21-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, maximum principle, apriori estimate, uniqueness, system of integral equations.
Mots-clés : Fourier transform, existence 
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S. Kh. Gekkieva; M. A. Kerefov. The boundary value problem for the generalized moisture transfer equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 1 (2018), pp. 21-31. http://geodesic.mathdoc.fr/item/VKAM_2018_1_a1/

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