Methods and Applications of Analysis

On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data

Yoshikazu Giga and Noriaki Umeda

Full-text: Open access

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.

Article information

Source
Methods Appl. Anal., Volume 15, Number 2 (2008), 185-196.

Dates
First available in Project Euclid: 13 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.maa/1234536493

Mathematical Reviews number (MathSciNet)
MR2481678

Zentralblatt MATH identifier
1170.35435

Subjects
Primary: 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations

Keywords
Instant blow-up local-in-time solution semilinear heat equation

Citation

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


Export citation