Global Boundedness in a Logarithmic Keller–Segel System

Jinyang Liu, Boping Tian, Deqi Wang (), Jiaxin Tang and Yujin Wu
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Jinyang Liu: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Boping Tian: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Deqi Wang: School of Statistics, Chengdu University of Information Technology, Chengdu 610103, China
Jiaxin Tang: School of Statistics, Chengdu University of Information Technology, Chengdu 610103, China
Yujin Wu: School of Economics and Management, Zhejiang Sci-Tech University, Hangzhou 310018, China

Mathematics, 2023, vol. 11, issue 12, 1-11

Abstract: In this paper, we propose a user-friendly integral inequality to study the coupled parabolic chemotaxis system with singular sensitivity under the Neumann boundary condition. Under a low diffusion rate, the classical solution of this system is uniformly bounded. Our proof replies on the construction of the energy functional containing ∫ Ω | v | 4 v 2 with v > 0 . It is noteworthy that the inequality used in the paper may be applied to study other chemotaxis systems.

Keywords: chemotaxis model; energy functional; integral inequality; global uniform boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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