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Short time behaviour of a singular solution to the heat equation with absorption

Published online by Cambridge University Press:  14 November 2011

R. E. Grundy  and
L. A. Peletier
R. E. Grundy
Affiliation:
Mathematical Institute, University of St Andrews, Scotland
L. A. Peletier
Affiliation:
The Mathematical Institute, University of Leiden, The Netherlands
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Synopsis

The paper considers the small time evolution of the interface which appears in the boundary value problem

A diffusion dominated small time outer expansion is not uniformly valid when x = O(t½ log t) and has to be supplemented by an inner expansion valid in a region where diffusion and absorption are of equal importance. For p < 1 a zero order inner solution is constructed, which is consistent with a moving interface where u is zero, and the small time development of this is given.

These results are first derived in a heuristic way using the method of matched expansions. However, an important aim of the paper is to give rigorous proofs, being one of the very few cases in nonlinear diffusion where this has been done.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 3-4 , 1987 , pp. 271 - 288
Copyright
Copyright © Royal Society of Edinburgh 1987

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