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

✍ Scribed by M.A. Herrero; E. Medina; J.J.L. Velázquez

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 928 KB
Volume: 97
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00104-6

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✦ Synopsis

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 chcmotaxis 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. (~) 1989 Elsevier Science B.V. All fights reserved.

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