Analysis of a Darcy Flow Model with a Dynamic Pressure Saturation Relation

We consider a new model for groundwater flow. The model differs from previous models in that the saturation-pressure relation is extended with a dynamic term, namely, the time derivative of the saturation. The resulting model equation is of nonlinear degenerate pseudoparabolic-type. We give a rigorous analysis of travelling wave solutions and the local behavior near fronts. Part of this analysis is then used in a formal asymptotic analysis of solutions with initial support in a half line. As an illustrative special case we also consider Heaviside initial data.