Methods and Applications of Analysis

Volume 15 (2008)

Number 2

On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data

Pages: 185 – 196

DOI: http://dx.doi.org/10.4310/MAA.2008.v15.n2.a5

Authors

Yoshikazu Giga

Noriaki Umeda

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.

Keywords

Instant blow-up; local-in-time solution; semilinear heat equation

2010 Mathematics Subject Classification

35K15, 35K55

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