Methods and Applications of Analysis
Volume 15 (2008)
On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data
Pages: 185 – 196
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.
Instant blow-up; local-in-time solution; semilinear heat equation
2010 Mathematics Subject Classification