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Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China

Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China

E-mail Address: 597746385@qq.com

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Bin Liu

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China

Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, Hubei, P. R. China

E-mail Address: binliu@mail.hust.edu.cn

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https://doi.org/10.1142/S0218202521500238Cited by:25 (Source: Crossref)

Abstract

In this work, we consider the two-species chemotaxis system with Lotka–Volterra competitive kinetics in a bounded domain with smooth boundary. We construct weak solutions and prove that they become smooth after some waiting time. In addition, the asymptotic behavior of the solutions is studied. Our results generalize some well-known results in the literature.

Communicated by M. Winkler

Keywords:

AMSC: 35D30, 35A01, 35Q92, 35B40, 92C17

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