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Non-axial self-similar hole filling for the porous medium equation

Authors: S. B. Angenent and D. G. Aronson
Journal: J. Amer. Math. Soc. 14 (2001), 737-782
MSC (2000): Primary 35K65, 37G99; Secondary 35K55, 76S05
Published electronically: May 30, 2001
MathSciNet review: 1839916
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Abstract | References | Similar Articles | Additional Information


We construct non-axially symmetric self-similar solutions to the porous medium equation by showing that the family of radial self-similar solutions found by Aronson and Graveleau (1993) undergoes a sequence of symmetry breaking bifurcations as the parameter $m$ decreases from $m=\infty$ to $m=1$.

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Additional Information

S. B. Angenent
Affiliation: Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin 53706

D. G. Aronson
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Keywords: Porous medium equation, self-similar solutions, symmetry breaking bifurcation
Received by editor(s): November 1, 1999
Published electronically: May 30, 2001
Additional Notes: The first author was supported by the National Science Foundation
Article copyright: © Copyright 2001 American Mathematical Society