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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:(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
Volume145
Issue number5
Early online date24 Aug 2015
DOIs
Publication statusPublished - Oct 2015

Fingerprint

Semilinear Heat Equation
Blow-up
Figure
Subspace
Finite Time Blow-up
Neumann Boundary Conditions
Compact Set
Strictly
Asymptotic Behavior
Zero
Term
Estimate

Keywords

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

Cite this

Global blow-up for a semilinear heat equation on a subspace. / Budd, C. J.; Dold, J. W.; Galaktionov, V. A.

In: Proceedings of the Royal Society of Edinburgh Section A - Mathematics, Vol. 145, No. 5, 10.2015, p. 893 - 923.

Research output: Contribution to journalArticle

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AU - Dold, J. W.

AU - Galaktionov, V. A.

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AB - 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).

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KW - global blow-up

KW - integral constraint

KW - non-local parabolic equation

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