Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Jin, Hai-Yang¹  Li, Jingyu^2,3  Wang, Zhi-An¹ 

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

[2] E China Normal Univ, Ctr Partial Differential Equat, Shanghai 200241, Peoples R China

[3] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

关键词: Chemotaxis;    Traveling wave solutions;    Linear instability;    Nonlinear stability;    Weighted energy estimates;   

DOI  :  10.1016/j.jde.2013.04.002

来源: Elsevier

【 摘 要 】

This paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis model with singular (or logarithmic) sensitivity and its transformed parabolic-hyperbolic system. Depending on the parameter signs, we discuss the linear instability of traveling wave solutions using the spectral analysis and nonlinear asymptotic stability of traveling wave solutions with zero end state by the weighted energy estimates, where the latter result solves the open question left in a previous work (Li and Wang, 2009 [7]). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free