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

This work is concerned with the following system: ▪ 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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 1998-09, Vol.97 (1), p.99-119
Main Authors: Herrero, M.A., Medina, E., Velázquez, J.J.L.
Format: Article
Language:English
Subjects:
Blow-up
Matched asymptotic expansions
Reaction-diffusion systems
Self-similar behaviour
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Summary:This work is concerned with the following system: ▪ 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.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(98)00104-6