Electron. J. Diff. Equ., Vol. 2014 (2014), No. 49, pp. 1-13.

Mathematical models of a liquid filtration from reservoirs

Anvarbek Meirmanov, Nelly Erygina, Saltanbek Mukhambetzhanov

This article studies the filtration from reservoirs into porous media under gravity. We start with the exact mathematical model at the microscopic level, describing the joint motion of a liquid in reservoir and the same liquid and the elastic solid skeleton in the porous medium. Then using a homogenization procedure we derive the chain of macroscopic models from the poroelasticity equations up to the simplest Darcy's law in the porous medium and hydraulics in the reservoir.

Submitted January 6, 2014. Published February 19, 2014.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Lame's equation; Stokes equation; liquid filtration; homogenization; poroelasticity.

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Anvarbek Meirmanov
Department of higher mathematics and cybernetics
Kazakh-British Technical University
Toli Bi 59, 050000, Almaty, Kazakhstan
email: anvarbek@list.ru
Nelly Erygina
Department of mathematics, Belgorod State University
ul.Pobedi 85, 308015 Belgorod, Russia
email: eryginan@bsu.edu.ru
Saltanbek Mukhambetzhanov
Department of differential equations
Al-Farabi Kazakh National University
Al-Farabi 71, 050000, Almaty, Kazakhstan
email: mukhambetzhanov@mail.ru

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