A further study on an attraction-repulsion chemotaxis system with logistic source

Wanjuan Du; Wanjuan Du

doi:10.3934/math.2024822

AIMS Mathematics

2024, Volume 9, Issue 7: 16924-16930. doi: 10.3934/math.2024822

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Research article

A further study on an attraction-repulsion chemotaxis system with logistic source

Wanjuan Du ^,

College of Mathematics Education, China West Normal University, Nanchong 637009, China

Received: 25 February 2024 Revised: 26 April 2024 Accepted: 29 April 2024 Published: 15 May 2024
MSC : 35B35, 35K55

This paper is concerned with the attraction-repulsion chemotaxis system (1.1) define on a bounded domain $ \Omega \subset \mathbb{R}^N(N\geq 1) $ with no-flux boundary conditions. The source function $ f $ in this system is a smooth function $ f $ that satisfies $ f(u)\leq a-bu^\eta $ for $ u\geq0 $. It is proven that $ \eta\geq1 $ is sufficient to ensure the boundedness of the solution when $ r < \frac{4(N+1)}{N(N+2)} $ is in the balance case $ \chi\alpha = \xi\gamma $, which improve the relevant results presented in papers such as Li and Xiang (2016), Xu and Zheng (2018), Xie and Zheng (2021), and Tang, Zheng and Li (2023).
- attraction-repulsion,
- boundedness,
- logistic source,
- chemotaxis
Citation: Wanjuan Du. A further study on an attraction-repulsion chemotaxis system with logistic source[J]. AIMS Mathematics, 2024, 9(7): 16924-16930. doi: 10.3934/math.2024822

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Abstract

This paper is concerned with the attraction-repulsion chemotaxis system (1.1) define on a bounded domain $ \Omega \subset \mathbb{R}^N(N\geq 1) $ with no-flux boundary conditions. The source function $ f $ in this system is a smooth function $ f $ that satisfies $ f(u)\leq a-bu^\eta $ for $ u\geq0 $. It is proven that $ \eta\geq1 $ is sufficient to ensure the boundedness of the solution when $ r < \frac{4(N+1)}{N(N+2)} $ is in the balance case $ \chi\alpha = \xi\gamma $, which improve the relevant results presented in papers such as Li and Xiang (2016), Xu and Zheng (2018), Xie and Zheng (2021), and Tang, Zheng and Li (2023).

References

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