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June 2008 On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data
Yoshikazu Giga, Noriaki Umeda
Methods Appl. Anal. 15(2): 185-196 (June 2008).

Abstract

For a semilinear heat equation admitting blow-up solutions a sufficient condition for nonexistence of local-in-time solutions are obtained. In particular, it is shown that if an initial data tends to infinity at space infinity then there is no local-in-time solution. As an application if the solution blows up at space infinity with least blow-up time, the solution cannot be extendable after blow-up time.

Citation

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Yoshikazu Giga. Noriaki Umeda. "On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data." Methods Appl. Anal. 15 (2) 185 - 196, June 2008.

Information

Published: June 2008
First available in Project Euclid: 13 February 2009

zbMATH: 1170.35435
MathSciNet: MR2481678

Subjects:
Primary: 35K15, 35K55

Rights: Copyright © 2008 International Press of Boston

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Vol.15 • No. 2 • June 2008
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