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Self-similarity in the post-focussing regime in porous medium flows

Published online by Cambridge University Press:  26 September 2008

S. B. Angenent  and
D. G. Aronson
S. B. Angenent
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA
D. G. Aronson
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

In the focussing problem for the porous medium equation, one considers an initial distribution of material outside some compact set K. As time progresses material flows into K, and at some finite time T first covers all of K. For radially symmetric flows, with K a ball centred at the origin, it is known that the intermediate asymptotics of this focussing process is described by a family of self-similar solutions to the porous medium equation. Here we study the postfocussing regime and show that its onset is also described by self-similar solutions, even for nonsymmetric flows.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 3 , June 1996 , pp. 277 - 285
Copyright
Copyright © Cambridge University Press 1996

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