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Self-similar blow-up for a reaction-diffusion system

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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


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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
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
Deposited On:31 Oct 2012 09:24
Last Modified:12 Dec 2018 15:07

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