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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Non-axial self-similar hole filling for the porous medium equation
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by S. B. Angenent and D. G. Aronson PDF
J. Amer. Math. Soc. 14 (2001), 737-782 Request permission


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
  • MR Author ID: 26245
  • ORCID: 0000-0003-3515-4539
  • Email:
  • D. G. Aronson
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • MR Author ID: 27340
  • Email:
  • Received by editor(s): November 1, 1999
  • Published electronically: May 30, 2001
  • Additional Notes: The first author was supported by the National Science Foundation
  • © Copyright 2001 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 737-782
  • MSC (2000): Primary 35K65, 37G99; Secondary 35K55, 76S05
  • DOI:
  • MathSciNet review: 1839916