Upscaling for a Degenerate and Coupled Parabolic System Arising from Fluid and Heat Transport in Heterogeneous Media

This contribution is devoted to the periodic homogenization of a system of nonlinear degenerate parabolic differential equations arising from the coupled fluid flow and heat transport through partially saturated porous media. We consider porous material exhibiting periodic spatial oscillations and present some a-priori estimates for the weak solutions (of the meso-scale problem) with respect to the scale parameter c, which are sufficient for passing to the limit epsilon -> 0 (as the oscillation period vanishes). Under the real assumptions on transport coefficients, we obtain the homogenized equations based on the two-scale convergence theory.