### Abstract

We estimate the blow-up time for the reaction diffusion equation u _{t} = ?u+?f(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here ?>?*, where ?* is the 'extremal' (critical) value for ?, such that there exists an 'extremal' weak but not a classical steady-state solution at ? = ?* with ||w(?)||_{8} ? infin; as 0<? ? ?*-. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s) = e^{s}, for ? - ?* «1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.

Original language | English |
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Pages (from-to) | 1507-1526 |

Number of pages | 20 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 30 |

Issue number | 13 |

DOIs | |

Publication status | Published - 10 Sep 2007 |

### Keywords

- Blow-up time estimates
- Boundary-layer theory
- Reaction diffusion equation

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## Cite this

*Mathematical Methods in the Applied Sciences*,

*30*(13), 1507-1526. https://doi.org/10.1002/mma.854