Geodesic
A priori estimate for solution of the
News of the Kabardin-Balkar scientific center of RAS, no. 6-1 (2018), pp. 28-32.

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Moisture movement in capillary porous media is described by the equation of Halliers' [1]. Boundary value problems for classical Halliers' equation are studied in paper [2]. However, in describing the properties of the moisture movement process in media with fractal structure, the models described by the fractional equations are most effective. Solution of boundary value problem for the fractional Halliers' equation in differential setting is studied. By using the method of energy inequalities for the solution of the problem we obtain a priori estimates.
Keywords: fractional derivative, a priori estimate
Mots-clés : Halliers' equation. 
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Ph. A. Karova. A priori estimate for solution of the. News of the Kabardin-Balkar scientific center of RAS, no. 6-1 (2018), pp. 28-32. http://geodesic.mathdoc.fr/item/IZKAB_2018_6-1_a4/

[1] A. F. Chudnovskii, Teplofizika pochv, Nauka, M., 1976, 137 pp.

[2] M. Kh. Shkhanukov-Lafishev, “O kraevykh zadachakh dlya uravneniya tretego poryadka”, Differents. uravneniya, 18:4 (1982), 1785–1795

[3] A. A. Alikhanov, “Boundary value problems for the diffusion equation of the variable order in differential and difference settings”, Appl. Math. Comput., 219 (2012), 3938–3946

[4] A. A. Alikhanov, “Apriornye otsenki reshenii kraevykh zadach dlya uravnenii drobnogo poryadka”, Differents. uravneniya, 46:5 (2010), 658–664