Dynamics for a two-species competitive Keller-Segel chemotaxis system with a free boundary. (English) Zbl 1467.35362
Summary: 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: \(0<a_1<1\leq a_2\), and weak competition case: \(0<a_1\), \(a_2<1\). Finally, an obstructed spreading case has been found, which could happen due to the effect of the chemotaxis.
MSC:
| 35R35 | Free boundary problems for PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
| 92C17 | Cell movement (chemotaxis, etc.) |
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