Homogenization of degenerate coupled transport processes in porous media with memory terms

In this paper, we establish a homogenization result for a doubly nonlinear parabolic system arising from the hygro-thermo-chemical processes in porous media taking into account memory phenomena. We present a mesoscale model of the composite (heterogeneous) material where each component is considered as a porous system and the voids of the skeleton are partially saturated with liquid water. It is shown that the solution of the mesoscale problem is two-scale convergent to that of the upscaled problem as the spatial parameter goes to zero.