Abstract:
This is a joint work with Esther Daus (D-fine, Vienna, Austria) and Nicola Zamponi (University of Ulm, Germany).
We present a model describing the infiltration of contaminants into the upper layers of an unsaturated soil, where the water phase consists of a mixture of chemical components subject to cross-diffusion effects. We show the existence of variational entropy solutions for a non-isothermal, immiscible, compressible Richards model with dynamic capillary pressure in porous media with large data. The primary variables are the mass concentrations of the components, the temperature and the water saturation of the porous medium.
To overcome the lack of parabolicity in the equations due to cross-diffusion, we begin by proving the existence of solutions for an approximate system that is uniformly elliptic with respect to the entropy variables. A priori estimates are derived from the entropy balance and the total energy balance equation, while compactness is achieved using the div-curl lemma. We point out that the dynamic capillary pressure allows us to obtain the bound for the time derivative of saturation, which is crucial for the compactness argument.