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



Yoshikazu Giga

Noriaki Umeda


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

35K15, 35K55

Published 1 January 2008