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Nonstationary filtration in partially saturated porous media

Published online by Cambridge University Press:  26 September 2008

Xinfu Chen ,
Avner Friedman  and
Tsuyoshi Kimura
Xinfu Chen
Affiliation:
University of Pittsburgh, Department of Mathematics and Statistics, Pittsburgh, PA 15260, USA (e-mal [email protected])
Avner Friedman
Affiliation:
University of Minnesota, Institute for Mathematics and its Applications, Minneapolis, MN 55455
Tsuyoshi Kimura
Affiliation:
Kao Corporation, Institute for Knowledge and Intelligence Science, Bunka 2-1-3, Sumida-ku, Tokyo 131, Japan
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Abstract

Nonstationary two-dimensional filtration in a porous medium is considered, whereby part of the medium is saturated, another part is unsaturated but wet, and the remaining part is dry. The saturated/unsaturated and unsaturated/dry interfaces are free boundaries. It is shown that there exists a unique solution, and that the saturation function is continuous in the wet portion of the medium; this implies that the two interfaces are separated. Under some monotonicity-type conditions on the initial and boundary data it is shown that the free boundaries are continuous.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 3 , September 1994 , pp. 405 - 429
Copyright
Copyright © Cambridge University Press 1994

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