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On convergence to equilibria for a chemotaxis model with volume-filling effect

In this paper, we study the asymptotic behavior of solutions to a chemotaxis model with volume-filling effect subject to the homogeneous Neumann boundary conditions. We establish a non-smooth version of eojasiewicz-Simon inequality, and we prove that as time goes to infinity the solution to our system converges to an equilibrium in W 1,p (Ω) × W 1,p (Ω), p> max(n ,2 ),Ω ⊂ R n . We also obtain an estimate of the decay rate to equilibrium.