Anvarbek Meirmanov, Nelly Erygina, Saltanbek Mukhambetzhanov
Abstract:
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 |
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Nelly Erygina Department of mathematics, Belgorod State University ul.Pobedi 85, 308015 Belgorod, Russia email: eryginan@bsu.edu.ru |
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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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