Abstract
In this paper, we investigate a two-species competitive chemotaxis Keller-Segel system equipped with a free boundary. The local existence and global existence of classical solutions are established, and then the asymptotic behavior of the solutions is described. Some spreading-vanishing dichotomies have been obtained both for the strong competition case: 0<a1<1≤a2, and weak competition case: 0<a1, a2<1. Finally, an obstructed spreading case has been found, which could happen due to the effect of the chemotaxis.
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