Blow-up of positive solutions of a semilinear parabolic equation with a gradient term

Miroslav Chlebík, Marek Fila, and Pavol Quittner

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Submission date: 07. Feb. 2003
Pages: 15
published in: Dynamics of continuous, discrete and impulsive systems, 10 (2003) 4, p. 525-537 
Bibtex
MSC-Numbers: 35B40, 35K60
Keywords and phrases: semilinear parabolic equation, nonlinear gradient term, blow-up rate and profile
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Abstract:
We study the blow-up behavior (in time and space) of positive solutions of a semilinear parabolic equation with a gradient term. Our main result is a sharp estimate for the spatial blow-up profile of radially decreasing solution on a ball. This result illustartes the influence of the gradient term on the profile.