We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers' diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we first obtain well-posedness results.

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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Cuesta Romero, C., & Hulshof, J. (2001). A model problem for unsaturated porous media flow with dynamic capillary pressure. Modelling, Analysis and Simulation [MAS]. CWI.