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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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:

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
Email: angenent@math.wisc.edu

D. G. Aronson
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: don@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-01-00372-1
PII: S 0894-0347(01)00372-1
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