Degenerate two-phase porous media flow model with dynamic capillarity

In this paper, we investigate a degenerate elliptic–parabolic system which describes the flow of two incompressible, immiscible fluids in porous media and including dynamic effects in the phase-pressure difference. First, for the regularized case, the existence and uniqueness of the weak solution are obtained. Then we let the regularization parameter go to zero to show the existence of weak solutions under degenerate case.