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

Abstract

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 Łojasiewicz–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⊂Rⁿ. We also obtain an estimate of the decay rate to equilibrium.