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Global and exponential attractor of the repulsive Keller–Segel model with logarithmic sensitivity

Published online by Cambridge University Press:  30 June 2020

LIN CHEN
Affiliation:
Department of Mathematics, Southwestern University of Finance and Economics, 555 Liutai Ave, Wenjiang, Chengdu, Sichuan611130, China, emails: lchen@smail.swufe.edu.cn; fzkong@smail.swufe.edu.cn; qwang@swufe.edu.cn
FANZE KONG
Affiliation:
Department of Mathematics, Southwestern University of Finance and Economics, 555 Liutai Ave, Wenjiang, Chengdu, Sichuan611130, China, emails: lchen@smail.swufe.edu.cn; fzkong@smail.swufe.edu.cn; qwang@swufe.edu.cn
QI WANG
Affiliation:
Department of Mathematics, Southwestern University of Finance and Economics, 555 Liutai Ave, Wenjiang, Chengdu, Sichuan611130, China, emails: lchen@smail.swufe.edu.cn; fzkong@smail.swufe.edu.cn; qwang@swufe.edu.cn

Abstract

We consider a Keller–Segel model that describes the cellular chemotactic movement away from repulsive chemical subject to logarithmic sensitivity function over a confined region in ${{\mathbb{R}}^n},\,n \le 2$ . This sensitivity function describes the empirically tested Weber–Fecher’s law of living organism’s perception of a physical stimulus. We prove that, regardless of chemotaxis strength and initial data, this repulsive system is globally well-posed and the constant solution is the global and exponential in time attractor. Our results confirm the ‘folklore’ that chemorepulsion inhibits the formation of non-trivial steady states within the logarithmic chemotaxis model, hence preventing cellular aggregation therein.

Type
Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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