Prevention of blow-up by fast diffusion in chemotaxis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:362

Article

Choi, Yung-Sze²  Wang, Zhi-an¹ 

[1] Univ Minnesota, Inst Math & Applicat, Minneapolis, MN 55455 USA

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

关键词: Chemotaxis;    Blow-up;    Fast diffusion;    Global existence;    Pattern formation;   

DOI  :  10.1016/j.jmaa.2009.08.012

来源: Elsevier

【 摘 要 】

In this paper, we study a strongly coupled parabolic system with cross diffusion term which models chemotaxis. The diffusion coefficient goes to infinity when cell density tends to an allowable maximum value. Such 'fast diffusion' leads to global existence of solutions in bounded domains for any given initial data irrespective of the spatial dimension, which is usually the goal of many modifications to the classical Keller-Segel model. The key estimates that make this possible have been obtained by a technique that uses ideas from Moser's iterations. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free