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 Swimshorts 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 HALVA ALMOND 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.