Complete and energy blow-up in indefinite superlinear parabolic problems

Julián López-Gómez; Pavol Quittner

doi:10.3934/dcds.2006.14.169

Article Contents

2006, Volume 14, Issue 1: 169-186. Doi: 10.3934/dcds.2006.14.169

This issue Previous Article Decay of correlations for non-Hölder observables for one-dimensional expanding Lorenz-like maps Next Article C *-algebras associated to dynamical systems

Complete and energy blow-up in indefinite superlinear parabolic problems

Julián López-Gómez^1, and
Pavol Quittner^2,

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

Received: March 31, 2004

Revised: January 31, 2005

Published: February 2006

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Indeﬁnite superlinear parabolic problems,
a priori estimates,
complete blow-up,
single-point blow-up.

Mathematics Subject Classification: 35B45, 35J65.

Citation:

Article Metrics

HTML views() PDF downloads(150) Cited by(0)

Complete and energy blow-up in indefinite superlinear parabolic problems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Complete and energy blow-up in indefinite superlinear parabolic problems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content