ASYMPTOTIC BEHAVIOR OF THE STOCHASTIC KELLER-SEGEL EQUATIONS

Discrete Continuous Dyn Syst Ser B. 2019 Mar;24(3):1367-1391. doi: 10.3934/dcdsb.2019020.

Abstract

This paper deals with the asymptotic behavior of the solutions of the non-autonomous one-dimensional stochastic Keller-Segel equations defined in a bounded interval with Neumann boundary conditions. We prove the existence and uniqueness of tempered pullback random attractors under certain conditions. We also establish the convergence of the solutions as well as the pullback random attractors of the stochastic equations as the intensity of noise approaches zero.

Keywords: Keller-Segel equations; asymptotic compactness; random attractor; upper semi-continuity.