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

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

doi:10.1017/S0308210515000256

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

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

University of Manchester

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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 language	English
Pages (from-to)	893 - 923
Number of pages	31
Journal	Proceedings of the Royal Society of Edinburgh Section A - Mathematics
Volume	145
Issue number	5
Early online date	24 Aug 2015
DOIs	https://doi.org/10.1017/S0308210515000256
Publication status	Published - Oct 2015

Keywords

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

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10.1017/S0308210515000256

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(C) 2015 Cambridge University Press. This is the author's accepted manuscript of an article published in Budd, CJ, Dold, JW & Galaktionov, VA 2015, 'Global blow-up for a semilinear heat equation on a subspace' Proceedings of the Royal Society of Edinburgh Section A - Mathematics, vol 145, no. 5, pp. 893 - 923., and available via: http://dx.doi.org/10.1017/S0308210515000256
Accepted author manuscript, 395 KB

Cite this

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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).",

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AU - Dold, J. W.

AU - Galaktionov, V. A.

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N2 - 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).

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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JO - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

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

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Chris Budd

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

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Chris Budd

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