Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (2): 125-131.doi: 10.16088/j.issn.1001-6600.2021061201

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Optimal Time-decay Rates of the Hyperbolic-parabolic System Modeling Chemotaxis in R3

WANG Han, ZHANG Yinghui*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2021-06-12 Revised:2021-07-02 Published:2022-05-31

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Abstract: The large-time behavior of solutions to the Cauchy problem of a 3D hyperbolic-parabolic system modeling chemotaxis is investigated. The optimal time decay rates of the higher-order spatial derivatives of the solutions are obtained. Compared with previous results, the main innovation of this paper is to give the highest order spatial derivative of the solutions which is the same as that of the heat equation. The proof is mainly based on low-frequency and high-frequency decomposition and delicate energy estimates.

Key words: hyperbolic-parabolic system, optimal decay rates, low-frequency and high-frequency decomposition, large-time behavior, chemotaxis

CLC Number: 

  • O29
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