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Global existence from single-component  estimates in a semilinear reaction-diffusion system
Author(s):
Pavol
Quittner;
Philippe
Souplet
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2719-2724.
MSC (1991):
Primary 35B60, 35K50, 35K60
Posted:
February 4, 2002
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Abstract:
For a system of two reaction-diffusion equations coupled by power nonlinearities, we prove that an  bound on a single component for suitable  is enough to guarantee global existence. Also we provide a strong indication that our condition on  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
Email:
quittner@fmph.uniba.sk
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
Email:
souplet@math.uvsq.fr
DOI:
10.1090/S0002-9939-02-06453-5
PII:
S 0002-9939(02)06453-5
Received by editor(s):
April 20, 2001
Posted:
February 4, 2002
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2002,
American Mathematical Society
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