Homogenization in the problems of nonlinear diffusion

The problem of diffusion and slow convection of admixtures in the absolutely rigid porous medium is considered. The Stokes equations for the compressible viscous fluid which occupies the porous space and convective diffusion equation are the base equations. Viscous of fluid is depends on the concentration of admixture. Numerical simulations on a such model are unrealistic due to the fact that its main differential equations involve non-smooth oscillatory coefficients, both big and small, under the differentiation operators. The rigorous justification is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results, we derive the nonlinear system consisting of Darcy's equations of filtration, where viscous of fluid depends on the concentration of admixture, and homogenized convective diffusion equation.