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

Xing Wu; Keqin Su

doi:10.3934/dcdsb.2021002

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2021, Volume 26, Issue 12: 6057-6068. Doi: 10.3934/dcdsb.2021002 open access

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

Xing Wu^, and
Keqin Su

College of Information and Management Science, Henan Agricultural University, Zhengzhou, Henan 450002, China

^* Corresponding author: Xing Wu
^* Corresponding author: Xing Wu

Received: July 31, 2020

Revised: October 31, 2020

Early access: December 2020

Published: December 2021

This work is partially supported by NSF of China (No.11801090)

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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 $ \dot{B}_{2, r}^{\frac d2}(\mathbb{R}^d)(1\leq r\leq \infty) $, we establish the global small solutions in multi-dimensional Besov space $ \dot{B}_{2, r}^{\frac d2-1}(\mathbb{R}^d) $ 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 $ B_{2, 1}^{\frac{d}{2}-1}(\mathbb{R}^d)\cap \dot{B}_{1, \infty}^0(\mathbb{R}^d) $.

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Mathematics Subject Classification: Primary:92C17, 35L52;Secondary:35B40.

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