Boundedness in a two-species chemotaxis-consumption system with nonlinear diffusion and sensitivity

摘要

This paper deals with the following two-species chemotaxis system with homogeneous Neumann boundary conditions and suitable initial conditions, where () is a bounded and smooth domain. Moreover, the parameters , and . For i = 1, 2, we assume that where , , and . Then if one of the following cases holds: ; and is sufficiently large, it is proved that the system possesses a unique global bounded classical solution.