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)