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

Article type: Research Article

Authors: Jiang, Jie | Zhang, Yanyan

Affiliations: School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China. E-mails: [email protected]; [email protected]

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 W1,p(Ω)×W1,p(Ω), p>max (n, 2), Ω⊂Rn. We also obtain an estimate of the decay rate to equilibrium.

Keywords: chemotaxis model, volume-filling effect, Łojasiewicz–Simon inequality

DOI: 10.3233/ASY-2009-0948

Journal: Asymptotic Analysis, vol. 65, no. 1-2, pp. 79-102, 2009