Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case

N. I. Kavallaris, A. A. Lacey, C. V. Nikolopoulos, D. E. Tzanetis

Research output: Contribution to journalArticle

Abstract

We estimate the blow-up time for the reaction diffusion equation u t = ?u+?f(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here ?>?*, where ?* is the 'extremal' (critical) value for ?, such that there exists an 'extremal' weak but not a classical steady-state solution at ? = ?* with ||w(?)||8 ? infin; as 0<? ? ?*-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s) = es, for ? - ?* «1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)1507-1526
Number of pages20
JournalMathematical Methods in the Applied Sciences
Volume30
Issue number13
DOIs
Publication statusPublished - 10 Sep 2007

Keywords

  • Blow-up time estimates
  • Boundary-layer theory
  • Reaction diffusion equation

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