Electron. J. Differential Equations, Vol. 2022 (2022), No. 58, pp. 1-17.

Boundedness and asymptotic stability in a chemotaxis model with indirect signal production and logistic source

Xiaobing Ye, Liangchen Wang

Abstract:
This article concerns the chemotaxis-growth system with indirect signal production

on a smooth bounded domain $\Omega\subset \mathbb{R}^n$ ($n\geq1$) with homogeneous Neumann boundary condition, where the parameters $\mu, \delta>0$. It is proved that if $n\leq 2$ and $\mu>0$, for all suitably regular initial data, this model possesses a unique global classical solution which is uniformly-in-time bounded. While in the case $n\geq 3$, we show that if $\mu$ is sufficiently large, this system possesses a global bounded solution. Furthermore, the large time behavior and rates of convergence have also been considered under some explicit conditions.

Submitted February 15, 2021. Published August 2, 2022.
Math Subject Classifications: 92C17, 35K35, 35A01, 35B35.
Key Words: Chemotaxis; boundedness; asymptotic behavior; indirect signal production.
DOI: https://doi.org/10.58997/ejde.2022.58

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Xiaobing Ye
School of Science
Chongqing University of Posts and Telecommunications
Chongqing 400065, China
email: xiaobingye1130@126.com
Liangchen Wang
School of Science
Chongqing University of Posts and Telecommunications
Chongqing 400065, China
email: wanglc@cqupt.edu.cn

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