This paper deals with the dynamical properties of the quasilinear parabolic-parabolic chemotaxis system
under homogeneous Neumann boundary conditions in a convex bounded domain
$ \begin{equation*} \begin{split} D(u)\geq (u+1)^{\alpha} \, \, \, \text{with}\, \, \, \alpha>0. \end{split} \end{equation*} $
It is shown that there is a positive constant
$ \begin{equation*} \begin{split} \int_{\Omega}u\geq m_{*} \end{split} \end{equation*} $
for all
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