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

C. J. Budd, J. W. Dold, V. A. Galaktionov

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

Original languageEnglish
Pages (from-to)893 - 923
Number of pages31
JournalProceedings of the Royal Society of Edinburgh Section A - Mathematics
Issue number5
Early online date24 Aug 2015
Publication statusPublished - Oct 2015


  • asymptotic behaviour
  • global blow-up
  • integral constraint
  • non-local parabolic equation


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