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.
|Title of host publication||Proceedings of the 4th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources (MAMERN'11, Saidia, Morocco, May 23-26, 2011)|
|Place of Publication||Granada|
|Publisher||Universidad de Granada|
|Publication status||Published - 2011|