Affiliations: Department of Mathematics, East China Normal University, Shanghai, P. R. China. E-mail: [email protected] | Institute of Mathematics, Fudan University, Shanghai, P. R. China. E-mail: [email protected]
Note: [] Corresponding author: Yanyan Zhang, Department of Mathematics, East China Normal University, Shanghai 200241, P. R. China. E-mail: [email protected]
Abstract: In this paper, a 1-d quasilinear nonuniform parabolic chemotaxis model with volume-filling effect is studied. The global existence and uniqueness of classical solution is proved. Furthermore, we prove that the global solution is uniformly bounded in time. With the help of a suitable non-smooth Simon–Łojasiewicz approach, we obtain the results on convergence of the solution to equilibrium and the convergence rate.
