Herrero, Miguel A. and Medina Reus, Elena and Velázquez, J.J. L.
(1997)
*Finite-time aggregation into a single point in a reaction-diffusion system.*
Nonlinearity, 10
(6).
pp. 1739-1754.
ISSN 0951-7715

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Official URL: http://iopscience.iop.org/0951-7715/10/6/016

## Abstract

We consider the following system: [GRAPHICS] which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial solutions that blow-up in a finite time. The asymptotic behaviour of such solutions is analysed in detail. In particular, we obtain that the profile of any such solution consists of an imploding, smoothed-out shock wave that collapses into a Dine mass when the singularity is formed. The differences between this type of behaviour and that known to occur for blowing-up solutions of (S) in the case N = 2 are also discussed.

Item Type: | Article |
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Uncontrolled Keywords: | Chemotaxis; equations; singularities; clusters |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 16970 |

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Deposited On: | 05 Nov 2012 11:29 |

Last Modified: | 07 Feb 2014 09:39 |

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