Electron. J. Diff. Equ., Vol. 2012 (2012), No. 105, pp. 1-16.

Mathematical models of a diffusion-convection in porous media

Anvarbek M. Meirmanov, Reshat Zimin

Abstract:
Mathematical models of a diffusion-convection 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 diffusion-convection 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 diffusion-convection in absolutely rigid porous media.

Submitted March 1, 2012. Published June 21, 2012.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Diffusion-convection; 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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