%0 Journal Article
%T Mathematical models of a diffusion-convection in porous media
%A Anvarbek M. Meirmanov
%A Reshat Zimin
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X 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.
%K Diffusion-convection
%K liquid filtration
%K homogenization
%U http://ejde.math.txstate.edu/Volumes/2012/105/abstr.html