Asymptotic stability in a chemotaxis-competition system with indirect signal production
Asymptotic stability in a chemotaxis-competition system with indirect signal production
This paper deals with a fully parabolic inter-species chemotaxis-competition system with indirect signal production \begin{document}$ \begin{eqnarray*} \label{1a} \left\{ \begin{split}{} &u_{t} = \text{div}(d_{u}\nabla u+\chi u\nabla w)+\mu_{1}u(1-u-a_{1}v), &(x,t)\in \Omega\times (0,\infty), \\ &v_{t} = d_{v}\Delta v+\mu_{2}v(1-v-a_{2}u), &(x,t)\in \Omega\times (0,\infty), \\ & w_{t} = d_{w}\Delta w-\lambda w+\alpha v, &(x,t)\in \Omega\times (0,\infty), \end{split} \right. \end{eqnarray*} …