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Global existence and asymptotic behavior of a two-species competitive Keller-Segel system on \(\mathbb{R}^N\). (English) Zbl 1481.92024

A system consisting of two parabolic equations and an elliptic one describing chemotaxis with competition of two species is considered in the whole space \(\mathbb R^N\). Compared to a well-studied case of bounded domains and homogeneous Neumann conditions, this leads to several additional difficulties in analysis. Results include local- and global-in-time existence of solutions with their convergence to steady states in some cases, e.g.if coexistence state exists, etc.

MSC:

92C17 Cell movement (chemotaxis, etc.)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35B40 Asymptotic behavior of solutions to PDEs
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