Herrero García, Miguel Ángel 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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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.
|Uncontrolled Keywords:||Reaction-diffusion systems; blow-up; self-similar behaviour; matched asymptotic expansions; chemotaxis; equations; aggregation; clusters; model|
|Subjects:||Sciences > Mathematics > Differential equations|
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|Deposited On:||31 Oct 2012 10:24|
|Last Modified:||31 Oct 2012 10:24|
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