## Self-Similar Solutions of a Nonlinear Heat Equation

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
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 $|x|\to \infty$.