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

Angenent, S.; Aronson, D.

doi:10.1090/S0894-0347-01-00372-1

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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
Posted: 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 decreases from $m=\infty$ to .

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