Existence of weak solutions to a degenerate pseudo-parabolic equation modeling two-phase flow in porous media

In this paper, we consider a degenerate pseudo-parabolic equation modeling two-phase flow in porous media, where dynamic effects in the difference of the phase pressures are included. Because of the special form of the capillary induced diffusion function, the equation becomes degenerate for certain values of the unknown. To overcome the diffculties due to the degeneracy, a regularization method is employed for proving the existence of a weak solution.