Abstract:
The heat-moisture transfer in soils is a fundamental base in addressing many problems of hydrology, agrophysics, building physics and other fields of science. The researchers focus on possibility of reflecting specific features of the studied arrays in the equations as well as their structure, physical properties, the processes going on in them, etc.
In view of this, there arises a new class of fractional differential equations of state and transport being the base for most mathematical models describing a wide class of physical and chemical processes in media with a fractal structure and memory.
This paper studies the Dirichlet boundary value problem for the Aller–Lykov moisture transfer equation with the Riemann–Liouville fractional derivative in time. The considered equation is a generalization of the Aller-Lykov equation obtained by means of introducing the concept of the fractal rate of humidity change, which accounts the presence of flows moving against the moisture potential.
The existence of the solution to the Dirichlet boundary value problem is proved by the Fourier method. By means of energy inequalities method, for the solution we obtain an apriori estimate in terms of fractional Riemann-Liouville derivative, which implies the uniqueness of the solution.
Citation:
S. Kh. Gekkieva, M. A. Kerefov, “Dirichlet boundary value problem for Aller–Lykov moisture transfer equation with fractional derivative in time”, Ufa Math. J., 11:2 (2019), 71–81
\Bibitem{GekKer19}
\by S.~Kh.~Gekkieva, M.~A.~Kerefov
\paper Dirichlet boundary value problem for Aller--Lykov moisture transfer equation with fractional derivative in time
\jour Ufa Math. J.
\yr 2019
\vol 11
\issue 2
\pages 71--81
\mathnet{http://mi.mathnet.ru/eng/ufa472}
\crossref{https://doi.org/10.13108/2019-11-2-71}
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Linking options:
https://www.mathnet.ru/eng/ufa472
https://doi.org/10.13108/2019-11-2-71
https://www.mathnet.ru/eng/ufa/v11/i2/p72
This publication is cited in the following 6 articles:
S. Kh. Gekkieva, M. A. Kerefov, “K voprosu suschestvovaniya resheniya pervoi kraevoi zadachi dlya uravneniya vlagoperenosa Allera – Lykova s operatorom drobnogo diskretno raspredelennogo differentsirovaniya”, Doklady AMAN, 24:1 (2024), 11–22
S.Kh. Gekkieva, M. A. Kerefov, F. M. Nakhusheva, “Local and nonlocal boundary value problems for generalized Aller–Lykov equation”, Ufa Math. J., 15:1 (2023), 21–33
B. Yu. Irgashev, “Mixed Problem for Higher-Order Equations with Fractional Derivative and Degeneration in Both Variables”, Ukr Math J, 74:10 (2023), 1513
Nasser Al-Salti, Erkinjon Karimov, Sebti Kerbal, “A boundary problem for the time-fractional Hallaire–Luikov moisture transfer equation with Hilfer derivative”, Comp. Appl. Math., 42:2 (2023)
B. Yu. Irgashev, “Mixed problem for higher-order equations with fractional derivative and degeneration in both variables”, Ukr. Mat. Zhurn., 74:10 (2022), 1328
M. A. Kerefov, S. Kh. Gekkieva, “Chislenno-analiticheskii metod resheniya kraevoi zadachi dlya obobschennykh uravnenii vlagoperenosa”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 19–34