Title: The unsaturated flow in porous media with dynamic capillary pressure,
Abstract: In this paper we consider a degenerate pseudoparabolic equation for the
wetting saturation of an unsaturated two-phase flow in porous media with
dynamic capillary pressure-saturation relationship where the relaxation
parameter depends on the saturation. Following the approach given in [12] the
existence of a weak solution is proved using Galerkin approximation and
regularization techniques. A priori estimates needed for passing to the limit
when the regularization parameter goes to zero are obtained by using
appropriate test-functions, motivated by the fact that considered PDE allows a
natural generalization of the classical Kullback entropy. Finally, a special
care was given in obtaining an estimate of the mixed derivative term by
combining the information from the capillary pressure with obtained a priori
estimates on the saturation.