Global boundedness in a Keller-Segel system with nonlinear indirect signal consumption mechanism by Zihan Zheng, Juan Wang, Liming Cai

“…In this paper, we study a quasilinear chemotaxis model with a nonlinear indirect consumption mechanism$ \begin{equation*} \left\{ \begin{array}{ll} v_{1t} = \nabla \cdot\big(\psi(v_{1})\nabla v_{1}-\chi \phi(v_{1})\nabla v_{2}\big)+\lambda_{1}v_{1}-\lambda_{2}v_{1}^{\beta},\ &\ \ x\in \Omega, \ t>0,\\[2.5mm] v_{2t} = \Delta v_{2}-w^{\theta}v_{2}, \ &\ \ x\in \Omega, \ t>0,\\[2.5mm] 0 = \Delta w-w+v_{1}^{\alpha}, \ &\ \ x\in \Omega, \ t>0 ,\\[2.5mm] \end{array} \right. …”
Get full text