A free boundary problem for an attraction–repulsion chemotaxis system

• Main Authors: Weiyi Zhang, Zuhan Liu, Ling Zhou
• Format: Article
• Language: English
• Published: SpringerOpen 2018-12-01
• Series: Boundary Value Problems
• Subjects: Attraction–repulsion chemotaxis system; Free boundary; Spreading and vanishing
• Online Access: http://link.springer.com/article/10.1186/s13661-018-1105-9

Abstract In this paper we study an attraction–repulsion chemotaxis system with a free boundary in one space dimension. First, under some conditions, we investigate existence, uniqueness and uniform estimates of the global solution. Next, we prove a spreading–vanishing dichotomy for this model. In the vanishing case, the species fail to establish and die out in the long run. In the spreading case, we provide some sufficient conditions to prove that the species successfully spread to infinity as t→∞ $t\rightarrow\infty$ and stabilize at a constant equilibrium state. The criteria for spreading and vanishing are also obtained.