American Institute of Mathematical Sciences

January  2006, 14(1): 169-186. doi: 10.3934/dcds.2006.14.169

Complete and energy blow-up in indefinite superlinear parabolic problems

 1 Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040-Madrid, Spain 2 Institute of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, 84248 Bratislava

Received  April 2004 Revised  February 2005 Published  October 2005

We study the continuation of solutions of superlinear indefinite parabolic problems after the blow-up time. The nonlinearity is of the form $a(x)u^p$, where $p>1$ is subcritical and $a$ changes sign. Unlike the case $a>0$, the solutions will never blow up completely in the whole domain but only in a certain subdomain. In some cases we give a precise description of this subdomain. We also derive sufficient conditions for the blow-up of the associated energy.
Citation: Julián López-Gómez, Pavol Quittner. Complete and energy blow-up in indefinite superlinear parabolic problems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (1) : 169-186. doi: 10.3934/dcds.2006.14.169
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