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

Angenent, S.; Aronson, D.

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

Non-axial self-similar hole filling for the porous medium equation
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by S. B. Angenent and D. G. Aronson

J. Amer. Math. Soc. 14 (2001), 737-782

DOI: https://doi.org/10.1090/S0894-0347-01-00372-1

Published electronically: May 30, 2001

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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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