Boundedness in a quasilinear fully parabolic two-species chemotaxis system of higher dimension
Boundedness in a quasilinear fully parabolic two-species chemotaxis system of higher dimension
This paper considers the following coupled chemotaxis system: $$\textstyle\begin{cases} u_{t}=\nabla\cdot(\phi(u)\nabla u)-\chi_{1} \nabla\cdot(u\nabla w)+\mu_{1} u(1-u-a_{1} v), \\ v_{t}=\nabla\cdot(\psi(v)\nabla v)-\chi_{2} \nabla\cdot(v\nabla w)+\mu_{2} v(1-a_{2}u-v), \\ w_{t}=\Delta w-\gamma w+\alpha u+\beta v, \end{cases} $$ with homogeneous Neumann boundary conditions in a bounded domain $\Omega\subset\mathbb{R}^{N}$ ( $N\ge3$ ) with smooth boundaries, where $\chi_{1}$ , $\chi_{2}$ , …