A 1-d quasilinear nonuniform parabolic chemotaxis model with volume-filling effect

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.