Methods and Applications of Analysis
- Methods Appl. Anal.
- Volume 15, Number 2 (2008), 185-196.
On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data
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.
Methods Appl. Anal., Volume 15, Number 2 (2008), 185-196.
First available in Project Euclid: 13 February 2009
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Giga, Yoshikazu; Umeda, Noriaki. On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data. Methods Appl. Anal. 15 (2008), no. 2, 185--196. https://projecteuclid.org/euclid.maa/1234536493