Pattern formation (I): The Keller-Segel model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Guo, Yan²  Hwang, Hyung Ju¹ 

[1] Pohang Univ Sci & Technol, Dept Math, Pohang 790784, South Korea

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

关键词: Keller-Segel;    Chemotaxis;    Pattern formation;    Instability;    Nonlinear dynamics;   

DOI  :  10.1016/j.jde.2010.07.025

来源: Elsevier

【 摘 要 】

We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude delta, we prove that its nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of fastest growing modes, over a time period of In 1/delta. Our result can be interpreted as a rigorous mathematical characterization for early pattern formation in the Keller-Segel model. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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