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Asymptotic stability of the one-dimensional attraction-repulsion chemotaxis system
  • Aichao Liu,
  • Lufang Mi
Aichao Liu
Shandong University of Aeronautics
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Lufang Mi
Shandong University of Aeronautics

Corresponding Author:milufang@126.com

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Abstract

The asymptotic stability of the one-dimensional attraction-repulsion chemotaxis system is concerned with in this paper. First of all, we get the globally bounded classical solutions of the system with initial data ( u 0 , v 0 , ω 0 ) ∈ ( W 1 , ∞ ( Ω ) ) 3 . Next, by constructing an appropriate Lyapunov function, we also show that the solutions converge exponentially to the constant steady state ( u ̵̄ 0 , α β u ̵̄ 0 , γ δ u ̵̄ 0 ) if ξγ χα > max { β δ , δ β } . It is worth mentioning that Jin and Wang (2015) showed that the solutions converge algebraically to the constant steady state under conditions β= δ and ξγχα<0, and our results filled the gap in the ξγχα>0.
31 Aug 2024Submitted to Mathematical Methods in the Applied Sciences
02 Sep 2024Submission Checks Completed
02 Sep 2024Assigned to Editor
06 Sep 2024Review(s) Completed, Editorial Evaluation Pending
06 Sep 2024Reviewer(s) Assigned