Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF PERIODIC SOLUTIONS TO A FRACTIONAL CHEMOTAXIS SYSTEM ON THE WEAKLY COMPETITIVE CASE

  • Lei, Yuzhu (School of Mathematical Science Yangzhou University) ;
  • Liu, Zuhan (School of Mathematical Science Yangzhou University) ;
  • Zhou, Ling (School of Mathematical Science Yangzhou University)
  • Received : 2019.11.03
  • Accepted : 2020.07.17
  • Published : 2020.09.30
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Abstract

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p0, where p0 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

Acknowledgement

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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