caa a22 4500 38810872X CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500019351 doi S0308210500019351 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500019351 Matos J. Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France Convergence of blow-up solutions of nonlinear heat equations in the supercritical case [Elektronische Daten] [J. Matos] 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. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1197-1227 0308-2105 129:6<1197 1999 129 PRM https://doi.org/10.1017/S0308210500019351 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500019351 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Matos J. Laboratoire d'Analyse Numérique, Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1197-1227 0308-2105 129:6<1197 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge