Global existence and asymptotic behavior of periodic solutions to a fractional chemotaxis system on the weakly competitive case
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1269-1297
https://doi.org/10.4134/BKMS.b190980
Published online September 30, 2020
Yuzhu Lei, Zuhan Liu, Ling Zhou
Yangzhou University; Yangzhou University; Yangzhou University
Abstract : In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order $s\in(0,2)$. It is proved that for $s>2p_{0}$, where $p_{0}$ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.
Keywords : Fractional chemotaxis, Lotka-Volterra competition, global classical solution, asymptotic stability
MSC numbers : 35A01, 92B05, 35B40
Supported by : The work is partially supported by National Natural Science Foundation of China (11771380) and Natural Science Foundation of Jiangsu Province (BK20191436)
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