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Blow-up for a parabolic system coupled in an equation and a boundary condition

Published online by Cambridge University Press:  12 July 2007

Keng Deng  and
Cheng-Lin Zhao
Keng Deng
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
Cheng-Lin Zhao
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
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Abstract

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In this paper, we consider non-negative solutions of , We prove that if pq ≤ 1, every solution is global while if pq > 1, all solutions blow up in finite time. We also show that if p, q ≥ 1, then blow-up can occur only on the boundary.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 6 , December 2001 , pp. 1345 - 1355
Copyright
Copyright © Royal Society of Edinburgh 2001