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Finite-time aggregation into a single point in a reaction-diffusion system

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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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
Uncontrolled Keywords:Chemotaxis; equations; singularities; clusters
Subjects:Sciences > Mathematics > Differential equations
ID Code:16970
References:

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