Boundedness in a two species attraction-repulsion chemotaxis system with two chemicals

Aichao Liu; Binxiang Dai; Yuming Chen

doi:10.3934/dcdsb.2021306

Article Contents

2022, Volume 27, Issue 10: 6037-6062. Doi: 10.3934/dcdsb.2021306

This issue Previous Article On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation Next Article On weak (measure-valued)-strong uniqueness for compressible MHD system with non-monotone pressure law

Boundedness in a two species attraction-repulsion chemotaxis system with two chemicals

1.
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha 410083, China
2.
School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
3.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada

^* Corresponding author: Binxiang Dai and Yuming Chen
^* Corresponding author: Binxiang Dai and Yuming Chen

Received: April 30, 2021

Revised: October 31, 2021

Published: October 2022

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Abstract

This paper deals with a class of attraction-repulsion chemotaxis systems in a smoothly bounded domain. When the system is parabolic-elliptic-parabolic-elliptic and the domain is $ n $-dimensional, if the repulsion effect is strong enough then the solutions of the system are globally bounded. Meanwhile, when the system is fully parabolic and the domain is either one-dimensional or two-dimensional, the system also possesses a globally bounded classical solution.

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Mathematics Subject Classification: Primary: 35A01, 35Q92, 92C17.

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