Global asymptotic stability of steady states in a chemotaxis-growth system with singular sensitivity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Global asymptotic stability of steady states in a chemotaxis-growth system with singular sensitivity

Authors:	Pan Zheng Chunlai Mu Robert Willie Xuegang Hu

Affiliation:	1. Department of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China;3. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Westville Campus, 4001 Durban, South Africa

Abstract:	This paper deals with a fully parabolic chemotaxis-growth system with singular sensitivity $\{\begin{matrix} u_{t} = Δ u ? χ ? ? (u ? ln v) + r u ? μ u^{2}, & (x, t) \in Ω \times (0, \infty), \\ v_{t} = Δ v ? v + u, & (x, t) \in Ω \times (0, \infty), \end{matrix} is=$ under homogeneous Neumann boundary conditions in a smooth bounded domain $Ω ? R^{2}$ , where the parameters $χ, μ > 0$ and $r \in R$ . Global existence and boundedness of solutions to the above system were established under some suitable conditions by Zhao and Zheng (2017). The main aim of this paper is further to show the large time behavior of global solutions which cannot be derived in the previous work.

Keywords:	Asymptotic stability Chemotaxis Singular sensitivity
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