Self-Similar Solutions of a Nonlinear Heat Equation

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J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 3, Page 501--540.

Cazenave, Thierry ; Dickstein, FlÃ¡vio ; Miguel {\sc Escobedo}\ ; Weissler, Fred B.
Self-Similar Solutions of a Nonlinear Heat Equation
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
In this paper, we study the asymptotic behavior of certain solutions of the nonlinear heat equation $u_t-\Laplacian u+|u|^Î± u=0$ in $(0,\infty ) Ã \hbox{\ens R}^N $, where $Î± >0$. We focus especially on solutions that may change sign and that do not necessarily have a radial behavior as $|x|\to \infty $.

Mathematics Subject Classification (1991): 35K05, 35K15, 35B40

Mathematical Reviews Number: MR1855457

Received: 2001-01-15

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