Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary. II. Spreading-vanishing dichotomy in a domain with a free boundary

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Bao, Lianzhang^1,2  Shen, Wenxian² 

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

关键词: Chemoattraction-repulsion system;    Nonlinear parabolic equations;    Free boundary problem;    Spreading-vanishing dichotomy;    Invasive population;   

DOI  :  10.1016/j.jde.2020.03.004

来源: Elsevier

【 摘 要 】

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. In this first of the series, we investigated the dynamical behaviors of logistic type chemotaxis models on the half line R+, which are formally corresponding limit systems of the free boundary problems. In the second of the series, we establish the spreading-vanishing dichotomy in chemoattraction-repulsion systems with a free boundary as well as with double free boundaries. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free