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Infiltration in porous media with dynamic capillary pressure: Travelling waves. (English) Zbl 0970.76096
Summary: 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.

MSC:
76S05 Flows in porous media; filtration; seepage
35Q53 KdV equations (Korteweg-de Vries equations)
86A05 Hydrology, hydrography, oceanography
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