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2008 The global profile of blow-up at space infinity in semilinear heat equations
Masahiko Shimojō
J. Math. Kyoto Univ. 48(2): 339-361 (2008). DOI: 10.1215/kjm/1250271415

Abstract

We consider semilinear heat equations on ${\mathbb{R}}^N$ and discuss the blow-up of solutions that occurs only at space infinity. We give sufficient conditions for such phenomena, and study the global profile of solutions at the blow-up time. Among other things, we establish a nearly optimal upper bound for the blow-up profile, which shows that the profile $u(x,T)$ cannot grow too fast as $|x|\to \infty$. We also prove that such blow-up is always complete.

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Masahiko Shimojō. "The global profile of blow-up at space infinity in semilinear heat equations." J. Math. Kyoto Univ. 48 (2) 339 - 361, 2008. https://doi.org/10.1215/kjm/1250271415

Information

Published: 2008
First available in Project Euclid: 14 August 2009

zbMATH: 1184.35078
MathSciNet: MR2436740
Digital Object Identifier: 10.1215/kjm/1250271415

Rights: Copyright © 2008 Kyoto University

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Vol.48 • No. 2 • 2008
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