Non-axial self-similar hole filling for the porous medium equation-Reference-Cited by-同舟云学术

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

Published:2001-05-30 Issue:4 Volume:14 Page:737-782
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Angenent S.,Aronson D.

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 m decreases from m = ∞ m=\infty to m = 1 m=1 .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2001-14-04/S0894-0347-01-00372-1/S0894-0347-01-00372-1.pdf

Reference23 articles.

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2. Intermediate asymptotics for convergent viscous gravity currents;Angenent, S. B.;Phys. Fluids,1995

3. Régularité des solutions de l’équation des milieux poreux dans 𝑅^{𝑁};Aronson, Donald G.;C. R. Acad. Sci. Paris S\'{e}r. A-B,1979

4. The porous medium equation;Aronson, D. G.,1986

5. Limit behaviour of focusing solutions to nonlinear diffusions;Aronson, D. G.;Comm. Partial Differential Equations,1998

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