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Infiltration in porous media with dynamic capillary pressure: travelling waves

Published online by Cambridge University Press:  23 October 2000

C. CUESTA ,
C. J. van DUIJN  and
J. HULSHOF
C. CUESTA
Affiliation:
CWI, P.O Box 94079, 1090 GB Amsterdam, The Netherlands (email: {carlota,hansd}@cwi.nl)
C. J. van DUIJN
Affiliation:
CWI, P.O Box 94079, 1090 GB Amsterdam, The Netherlands (email: {carlota,hansd}@cwi.nl)
J. HULSHOF
Affiliation:
Mathematical Department of Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands (email: hulshof@wi.leidenuniv.nl)
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Abstract

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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.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 4 , September 2000 , pp. 381 - 397
Copyright
2000 Cambridge University Press