### Impacto

Herrero, Miguel A. and Medina Reus, Elena and Velázquez, J.J. L.
(1998)
*Self-similar blow-up for a reaction-diffusion system.*
Journal of Computational and Applied Mathematics, 97
(1-2).
pp. 99-119.
ISSN 0377-0427

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Official URL: http://www.sciencedirect.com/science/article/pii/S0377042798001046

## Abstract

This work is concerned with the following system: [GRAPHICS] which is a model to describe several phenomena in which aggregation plays a crucial role as, for instance, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters. When the space dimension N is equal to three, we show here that (S) has radial solutions with finite mass that blow-up in finite time in a self-similar manner. When N = 2, however, no radial solution with finite mass may give rise to self-similar blow-up.

Item Type: | Article |
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Uncontrolled Keywords: | Reaction-diffusion systems; blow-up; self-similar behaviour; matched asymptotic expansions; chemotaxis; equations; aggregation; clusters; model |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 16946 |

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Deposited On: | 31 Oct 2012 09:24 |

Last Modified: | 07 Feb 2014 09:38 |

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