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Global existence and optimal decay rate of solutions to hyperbolic chemotaxis system in Besov spaces

Xing Wu,Keqin Su

Published 2020 in Discrete & Continuous Dynamical Systems - B

ABSTRACT

In this paper, we study the qualitative behavior of hyperbolic system arising from chemotaxis models. Firstly, by establishing a new product estimates in multi-dimensional Besov space \begin{document}$ \dot{B}_{2, r}^{\frac d2}(\mathbb{R}^d)(1\leq r\leq \infty) $\end{document} , we establish the global small solutions in multi-dimensional Besov space \begin{document}$ \dot{B}_{2, r}^{\frac d2-1}(\mathbb{R}^d) $\end{document} by the method of energy estimates. Then we study the asymptotic behavior and obtain the optimal decay rate of the global solutions if the initial data are small in \begin{document}$ B_{2, 1}^{\frac{d}{2}-1}(\mathbb{R}^d)\cap \dot{B}_{1, \infty}^0(\mathbb{R}^d) $\end{document} .

PUBLICATION RECORD

  • Publication year

    2020

  • Venue

    Discrete & Continuous Dynamical Systems - B

  • Publication date

    Unknown publication date

  • Fields of study

    Mathematics, Physics

  • Identifiers
    DOI 10.3934/dcdsb.2021002
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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