Global existence and asymptotic behavior of a two-species competitive fractional chemotaxis system on $\mathbb{R}^N$

Abstract

In this paper, we investigate a two-species competitive fractional chemotaxis system on $\mathbb{R}^N.$ We first prove the local existence and uniqueness of classical solutions. Next, we establish a comparison principle for the fractional parabolic equation. By comparison principle, we prove the global existence and boundedness of classical solutions. Finally, we determine the asymptotic behaviors of global bounded classical solutions for three competition cases.