October  1999, 5(4): 905-928. doi: 10.3934/dcds.1999.5.905

Unfocused blow up solutions of semilinear parabolic equations

1. 

Laboratoire d'Analyse Numérique, Université Pierre et Marie curie, 4, Place Jussieu, 7525 Paris Cedex 05, France

Received  July 1998 Revised  June 1999 Published  July 1999

The aim of this paper is to study the blow up behavior of a radially symmetric solution $u$ of the semilinear parabolic equation

$u_t - \Delta u = |u|^{p-1} u, \quad x\in\Omega,\quad t\in [0,T]$,

$u(t,x)=0, x\in\partial\Omega, \quad t\in [0,T] $,

$u(0,x) =u_0(x),\quad x\in\Omega $,

around a blow up point other than its centre of symmetry. We assume that $\Omega$ is a ball in $\mathbb R^N$ or $\Omega =\mathbb R^N$, and $p>1$. We show that $u$ behave as of a one-dimensional problem was concerned, that is, the possible asymptotic behaviors and final time profiles around an unfocused blow up point are the ones corresponding to the case of dimesion $N=1$.

Citation: Júlia Matos. Unfocused blow up solutions of semilinear parabolic equations. Discrete and Continuous Dynamical Systems, 1999, 5 (4) : 905-928. doi: 10.3934/dcds.1999.5.905
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