On instant blow-up for semilinear heat equations with growing initial data
Preprint Series # 916
Giga, Yoshikazu and Umeda, Noriaki On instant blow-up for semilinear heat equations with growing initial data. (2008);
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.