### 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 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Global blow-up for a semilinear heat equation on a subspace'. Together they form a unique fingerprint.

## Profiles

### Chris Budd

- Department of Mathematical Sciences - Professor
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
- Probability Laboratory at Bath
- Centre for Doctoral Training in Decarbonisation of the Built Environment (dCarb)
- Centre for Mathematical Biology
- Institute for Mathematical Innovation (IMI)

Person: Research & Teaching

## Cite this

Budd, C. J., Dold, J. W., & Galaktionov, V. A. (2015). Global blow-up for a semilinear heat equation on a subspace.

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*,*145*(5), 893 - 923. https://doi.org/10.1017/S0308210515000256