Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 105, pp. 116.
Mathematical models of a diffusionconvection in porous media
Anvarbek M. Meirmanov, Reshat Zimin
Abstract:
Mathematical models of a diffusionconvection in porous media are derived
from the homogenization theory. We start with the mathematical model on
the microscopic level, which consist of the Stokes system for a weakly
compressible viscous liquid occupying a pore space, coupled with a
diffusionconvection equation for the admixture. We suppose that the
viscosity of the liquid depends on a concentration of the admixture and
for this nonlinear system we prove the global in time existence of a weak
solution. Next we rigorously fulfil the homogenization procedure as the
dimensionless size of pores tends to zero, while the porous body is
geometrically periodic. As a result, we derive new mathematical models of
a diffusionconvection in absolutely rigid porous media.
Submitted March 1, 2012. Published June 21, 2012.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Diffusionconvection; liquid filtration; homogenization
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Anvarbek M. Meirmanov
Department of mahtematics,
Belgorod State University
ul.Pobedi 85, 308015 Belgorod, Russia
email: meirmanov@bsu.edu.ru


Reshat Zimin
Department of mahtematics,
Belgorod State University
ul.Pobedi 85, 308015 Belgorod, Russia
email: reshat85@mail.ru

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