Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 1999 - Volume 129, Issue 06  

Research Article

Convergence of blow-up solutions of nonlinear heat equations in the supercritical case

J. Matosa1

a1 Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France

In this paper, we study the blow-up behaviour of the radially symmetric non-negative solutions u of the semilinear heat equation with supercritical power nonlinearity up (that is, (N – 2)p> N + 2). We prove the existence of non-trivial self-similar blow-up patterns of u around the blow-up point x = 0. This result follows from a convergence theorem for a nonlinear parabolic equation associated to the initial one after rescaling by similarity variables.

(Received March 09 1998)

(Accepted November 20 1998)