We consider a model for non-static groundwater flow where the saturation-pressure relation is extended by a dynamic term. This approach together with a convective term due to gravity, results in a pseudo-parabolic Burgers type equation. We give a rigorous study of global travelling wave solutions, with emphasis on the role played by the dynamic term and the appearance of fronts.

Ultraparabolic equations, pseudoparabolic equations, etc. (msc 35K70), Flows in porous media; filtration; seepage (msc 76S05), Two-phase and multiphase flows (msc 76Txx)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Cuesta Romero, C.M, van Duijn, C.J, & Hulshof, J. (1999). Infiltration in porous media with dynamic capillary pressure : travelling waves. Modelling, Analysis and Simulation [MAS]. CWI.