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Global existence and asymptotic behavior of periodic solutions to a fractional chemotaxis system on the weakly competitive case

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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.

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.

참고문헌 (49)

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