Sharp conditions for blowup of solutions of a chemotactical model for two species in R2

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:397

Article

Dickstein, Flavio

关键词: Keller-Segel;    Chemotaxis;    Two-species model;    Cauchy problem;    Radial solutions;    Blowup sharp criteria;   

DOI  :  10.1016/j.jmaa.2012.08.001

来源: Elsevier

【 摘 要 】

We consider a model system of Keller-Segel type for the evolution of two species in the whole space R-2 which are driven by chemotaxis and diffusion. It is well known that this problem admits global and blowup solutions. We show that there exists a sharp condition which allows to distinguish global and blowup solutions in the radially symmetric case. More precisely, let m(infinity), and n(infinity), be the total masses of the species. Then there exists a critical curve gamma in the m(infinity) - n(infinity) plane such that the solution blows up if and only if (m(infinity), n(infinity)) is above gamma. This gives an answer to a question raised by Conca et al. (2011) in [8]. We also study the asymptotic behaviour of global solutions in the subcritical case, showing that they are asymptotically self-similar. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free