Tohoku Mathematical Journal
2008
September
SECOND SERIES VOL. 60, NO. 3

Tohoku Math. J.
60 (2008), 303-328

Title NONCONSTANT SELFSIMILAR BLOW-UP PROFILE FOR THE EXPONENTIAL REACTION-DIFFUSION EQUATION

Author Marek Fila and Aappo Pulkkinen

(Received October 25, 2006, revised October 19, 2007)
Abstract. We study the blow-up profile of radial solutions of a semilinear heat equation with an exponential source term. Our main aim is to show that solutions which can be continued beyond blow-up possess a nonconstant selfsimilar blow-up profile. For some particular solutions we determine this profile precisely.

2000 Mathematics Subject Classification. Primary 35K57; Secondary 35B40.
Key words and phrases. Semilinear parabolic equation, blow-up profile, selfsimilar solutions.

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