Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling crossdiffusion which arises as a model for the consolidation of saturated porous media. Besides using energylike estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixedpoint principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-Time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.