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Solutions of the porous medium equation with degenerate interfaces

Published online by Cambridge University Press:  07 December 2012

J. IAIA  and
S. BETELU
J. IAIA
Affiliation:
University of North Texas, Denton, TX 76203, US emails: iaia@unt.edu, betelu@unt.edu
S. BETELU
Affiliation:
University of North Texas, Denton, TX 76203, US emails: iaia@unt.edu, betelu@unt.edu
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Abstract

We prove the existence of a one-parameter family of solutions of the porous medium equation in which the interface is a half line whose end point advances at a constant speed. Then we prove the stability of the solutions under a suitable class of perturbations. We discuss the relevance of these solutions to gravity-driven flows of thin films, and show that some solutions develop a very thin triangular plateau in the direction of propagation and that the angle of the plateau and its thickness are decreasing functions of the speed.

Keywords

Porous mediaGravity currentsThin filmsSingularities
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 3 , June 2013 , pp. 315 - 341
Copyright
Copyright © Cambridge University Press 2012

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