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Global Boundedness in a Logarithmic Keller–Segel System

Author

Listed:
  • Jinyang Liu

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    School of Statistics, Chengdu University of Information Technology, Chengdu 610103, 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)

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.

Suggested Citation

  • Jinyang Liu & Boping Tian & Deqi Wang & Jiaxin Tang & Yujin Wu, 2023. "Global Boundedness in a Logarithmic Keller–Segel System," Mathematics, MDPI, vol. 11(12), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2743-:d:1173080
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    References listed on IDEAS

    as
    1. Monica Marras & Giuseppe Viglialoro, 2018. "Boundedness in a fully parabolic chemotaxis‐consumption system with nonlinear diffusion and sensitivity, and logistic source," Mathematische Nachrichten, Wiley Blackwell, vol. 291(14-15), pages 2318-2333, October.
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