ANALYSIS OF A DARCY FLOW MODEL WITH A DYNAMIC PRESSURE SATURATION RELATION

We consider a new model for groundwater flow. The model differs from p revious models in that the saturation-pressure relation is extended wi th a dynamic term, namely, the time derivative of the saturation. The resulting model equation is of nonlinear degenerate pseudoparabolic-ty pe. We give a rigorous analysis of travelling wave solutions and the l ocal behavior near fronts. Part of this analysis is then used in a for mal asymptotic analysis of solutions with initial support in a half li ne. As an illustrative special case we also consider Heaviside initial data.