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Global existence from single-component $L_{p}$ estimates in a semilinear reaction-diffusion system

Authors: Pavol Quittner and Philippe Souplet
Journal: Proc. Amer. Math. Soc. 130 (2002), 2719-2724
MSC (1991): Primary 35B60, 35K50, 35K60
Published electronically: February 4, 2002
MathSciNet review: 1843418
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Abstract: For a system of two reaction-diffusion equations coupled by power nonlinearities, we prove that an $L_{p}$ bound on a single component for suitable $p$ is enough to guarantee global existence. Also we provide a strong indication that our condition on $p$ is the best possible. Moreover, this continuation result is in contrast with the corresponding necessary and sufficient conditions for local existence obtained earlier by the authors.

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Additional Information

Pavol Quittner
Affiliation: Institute of Applied Mathematics, Comenius University, Mlynská dolina, 84248 Bratislava, Slovakia

Philippe Souplet
Affiliation: Département de Mathématiques, INSSET, Université de Picardie, 02109 St-Quentin, France – and – Laboratoire de Mathématiques Appliquées, UMR CNRS 7641, Université de Versailles, 45 avenue des Etats-Unis, 78035 Versailles, France

Received by editor(s): April 20, 2001
Published electronically: February 4, 2002
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society

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