Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:384

Article

Winkler, Michael

关键词: Chemotaxis;    Logistic proliferation;    Blow-up;    Singularity formation;   

DOI  :  10.1016/j.jmaa.2011.05.057

来源: Elsevier

【 摘 要 】

We study radially symmetric solutions of a class of chemotaxis systems generalizing the prototype {u(t) = Delta u - x del . (u del v) + gimel u - mu u(kappa), x epsilon Omega, t > 0, 0 = Delta v - m(t) + u, x epsilon Omega, t > 0, in a ball Omega subset of R-n, with parameters x > 0, gimel >= 0, mu >= 0, and kappa > 1, and m(t) : = 1/vertical bar Omega vertical bar integral(Omega) u(x, t) u(x, t)dx. It is shown that when n >= 5 and kappa < 3/2 + 1/2n-2' then there exist initial data such that the smooth local-in-time solution of (*) blows up in finite time. This indicates that even superlinear growth restrictions may be insufficient to rule out a chemotactic collapse, as is known to occur in the corresponding system without any proliferation. (C) 2011 Elsevier Inc. All rights reserved.

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