An existence result related to two-phase flows with dynamical capillary pressure
Clément Cancès, Catherine Choquet, Yabin Fan, I. Pop · TU/e Research Portal · 2011
We consider a nonlinear degenerate pseudo-parabolic equation arising in the modeling of immiscible two-phase flows within porous media when the dynamic capillary pressure Pc = p(s) + T¿ts is a function of both the saturation s and its time derivative ¿ts. We show the existence of a weak solution to the problem using the compactness of a sequence of regularizations of the problem.