Self-Similar Solutions of a Nonlinear Heat Equation
Vol. 8 (2001), No. 3, Page 501--540.
Cazenave, Thierry ; Dickstein, Flávio ; Miguel {\sc Escobedo}\ ; Weissler, Fred B.
Self-Similar Solutions of a Nonlinear Heat Equation
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Abstract:
In this paper, we study the asymptotic behavior of certain solutions of the nonlinear heat equation $u_t-\Laplacian u+|u|^α u=0$ in $(0,\infty ) à \hbox{\ens R}^N $, where $α >0$. 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
