Geodesic
Boundary-value problem for the Aller--Lykov nonlocal moisture transfer equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 27-33

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In this paper, a boundary-value problem for the inhomogeneous Aller–Lykov moisture transfer equation with a fractional Riemann–Liouville time derivative is examined. The equation considered is a generalization of the Aller–Lykov equation obtained by introducing the fractal rate of change of humidity, which explains the appearance of flows directed against the potential of humidity. The existence of a solution to the first boundary-value problem is proved by the Fourier method. Using the method of energy inequalities for solutions of the problem, we obtain an a priori estimate in terms of the fractional Riemann–Liouville derivative, which implies the uniqueness of the solution.
Keywords: Aller–Lykov moisture transfer equation, Riemann–Liouville fractional derivative, Fourier method, a priori estimate, method of energy inequalities. 
@article{INTO_2019_167_a3,
     author = {S. Kh. Gekkieva and M. A. Kerefov},
     title = {Boundary-value problem for the {Aller--Lykov} nonlocal moisture transfer equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {27--33},
     publisher = {mathdoc},
     volume = {167},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_167_a3/}
}
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S. Kh. Gekkieva; M. A. Kerefov. Boundary-value problem for the Aller--Lykov nonlocal moisture transfer equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part III, Tome 167 (2019), pp. 27-33. http://geodesic.mathdoc.fr/item/INTO_2019_167_a3/