### 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 u_{0}(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 |
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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 | |

Publication status | Published - Oct 2015 |

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### 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.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*, vol. 145, no. 5, pp. 893 - 923. https://doi.org/10.1017/S0308210515000256

}

TY - JOUR

T1 - Global blow-up for a semilinear heat equation on a subspace

AU - Budd, C. J.

AU - Dold, J. W.

AU - Galaktionov, V. A.

PY - 2015/10

Y1 - 2015/10

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).

KW - asymptotic behaviour

KW - global blow-up

KW - integral constraint

KW - non-local parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=84939838934&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1017/S0308210515000256

U2 - 10.1017/S0308210515000256

DO - 10.1017/S0308210515000256

M3 - Article

VL - 145

SP - 893

EP - 923

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

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

SN - 0308-2105

IS - 5

ER -