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A probabilistic approach to blow-up of a semilinear heat equation

Published online by Cambridge University Press:  14 November 2011

Alison M. Etheridge
Alison M. Etheridge
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland, U.K.
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Abstract

We introduce a probabilistic approach to the study of blow-up of positive solutions to a class of semilinear heat equations. This then gives a representation of the coefficients in the power series expansion of the solutions. In a special case, this approach leads to a path-valued Markov process which can also be understood via the theory of Dawson-Watanabe superprocesses. We demonstrate the utility of the approach by proving a result on ‘complete blow-up’ of solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1235 - 1245
Copyright
Copyright © Royal Society of Edinburgh 1996

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