Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Li, Tong²  Wang, Zhi-An^1,3 

[1] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[3] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Keller-Segel model;    Chemotaxis;    Nonlinear stability;    Traveling waves;    Conservation law;    Large amplitude;    Energy estimates;   

DOI  :  10.1016/j.jde.2010.09.020

来源: Elsevier

【 摘 要 】

In this paper, we establish the existence and the nonlinear stability of traveling wave solutions to a system of conservation laws which is transformed, by a change of variable, from the well-known Keller-Segel model describing cell (bacteria) movement toward the concentration gradient of the chemical that is consumed by the cells. We prove the existence of traveling fronts by the phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without the smallness assumption on the wave strengths by the method of energy estimates. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free