Geodesic
Boundary value problem for the Aller--Lykov moisture transport generalized equation with concentrated heat capacity
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 23-29

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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.
Mots-clés : Aller's–Lykov equation
Keywords: fractional derivative, nonlocal problem, moisture transfer generalized equation, concentrated heat capacity, inequalities method, a priori estimate, boundary value problem. 
@article{VSGU_2018_24_3_a2,
     author = {M. A. Kerefov and F. M. Nakhusheva and S. Kh. Gekkieva},
     title = {Boundary value problem for the {Aller--Lykov} moisture transport generalized equation with concentrated heat capacity},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {23--29},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a2/}
}
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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 Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 24 (2018) no. 3, pp. 23-29. http://geodesic.mathdoc.fr/item/VSGU_2018_24_3_a2/