Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 105, pp. 1-16.
Title: Mathematical models of a diffusion-convection in porous media
Authors: Anvarbek M. Meirmanov (Belgorod State Univ., Russia)
Reshat Zimin (Belgorod State Univ., Russia)
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