Two-phase flow equations with outflow boundary conditions in the hydrophobic-hydrophilic case

We introduce an approximation procedure and provide existence results for two-phase flow equations in porous media. The medium can have hydrophobic and hydrophilic components such that the capillary pressure function is degenerate for extreme saturations. Our main interest is the outflow boundary condition which models an interface with open space. The approximate system introduces standard boundary conditions and can be used in numerical schemes. It allows the derivation of maximum principles. These are the basis for the derivation of the limiting system in the form of a variational inequality