Degenerate two-phase flow model in porous media including dynamics effects in the capillary pressure : existence of a weak solution

In this paper, we analyze a degenerate elliptic-parabolic system which describes the flow of two incompressible, immiscible fluids in porous media including dynamic effects in the phase-pressure difference. First, for a regularized diffusion coefficient, the existence and uniqueness of the weak solution in the non-degenerate case is obtained. Then we let the regularization parameter go to zero to show the existence of weak solutions under degenerate case. Keywords: Degeneracy, dynamic capillary pressure, two-phase flow, weak solution, uniqueness, pseudo-parabolic syste