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
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.
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