# American Institute of Mathematical Sciences

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doi: 10.3934/dcdsb.2021306
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## 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

Received  May 2021 Revised  November 2021 Early access January 2022

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.

Citation: Aichao Liu, Binxiang Dai, Yuming Chen. Boundedness in a two species attraction-repulsion chemotaxis system with two chemicals. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021306
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