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Large time behavior of solution to a parabolic-elliptic chemotaxis system with weak singular sensitivity and logistic kinetics: Boundedness, persistence, stability
This paper deals with the long-term behavior of positive solutions for the following parabolic-elliptic chemotaxis competition system with weak singular sensitivity and logistic source \begin{equation} \label{abstract-eq} \begin{cases} u_t=\Delta u-\chi \nabla\cdot (\frac{u}{v^{\lambda}} \nabla v) +ru- \mu u^2, \quad &x\in \Omega,\cr 0=\Delta v- \alpha v +\beta u,\quad &x\in \Omega, \cr \frac{\partial u}{\partial …