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.

Ultraparabolic equations, pseudoparabolic equations, etc. (msc 35K70), Flows in porous media; filtration; seepage (msc 76S05), Long-time behavior of solutions (msc 74H40)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

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