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Global blow-up for a semilinear heat equation on a subspace

Published online by Cambridge University Press:  24 August 2015

C. J. Budd
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK (mascjb@bath.ac.uk)
J. W. Dold
Affiliation:
School of Mathematics, Alan Turing Building, Upper Brook Street, University of Manchester, Manchester M13 9PL, UK (john.dold@manchester.ac.uk)
V. A. Galaktionov
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK (masvg@bath.ac.uk)

Abstract

We study the asymptotic behaviour as t → T, near a finite blow-up time T > 0, of decreasing-in-x solutions to the following semilinear heat equation with a non-local term:

with Neumann boundary conditions and strictly decreasing initial function u0(x) with zero mass. We prove sharp estimates for u(x, t) as t → T, revealing a non-uniform global blow-up:

uniformly on any compact set [δ, 1], δ ∈ (0, 1).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

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