Mathematical models of a diffusion-convection in porous media

Mathematical models of a diffusion-convection in porous media

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Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory.We start with the mathematical VITAMIN B-6 250 MG 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, Baby Cream while the porous body is geometrically periodic.As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous media.