Journal of the American Mathematical Society

Author(s): S. B. Angenent; D. G. Aronson
Journal: J. Amer. Math. Soc. 14 (2001), 737-782.
MSC (2000): Primary 35K65, 37G99; Secondary 35K55, 76S05
Posted: May 30, 2001
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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

decreases from $m=\infty$ to

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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 35K65, 37G99, 35K55, 76S05

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: 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
Posted: May 30, 2001
Additional Notes: The first author was supported by the National Science Foundation
Copyright of article: Copyright 2001, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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