Boundedness and stability for an indirect signal absorption chemotaxis system with signal-dependent motility

The paper is concerned with a chemotaxis system indirect signal absorption and signal-dependent motility$ \begin{equation*} \left\{ \begin{array}{lll} u_t = \Delta(\gamma(v)u), &x \in \Omega, t>0,\\ v_t \Delta v - vw, &x\in \tau w_t -\delta w+u, t>0, \end{array} \right. \end{equation*} $under the homogeneous Neumann boundary condition, where $ \Omega\subset R^n (n \geq 1) $, parameters \delta,\tau>0 $. \gamma(v) motility function. It shown that in n-dimensional smooth bounded domains n\leq2 or n\geq3 suitable initial data, some appropriate assumptions on ensure global existence stability of classical solution.