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.

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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

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