Asymptotic attractors of Benjamin-Bona-Mahony equations

Abstract

In this paper, we consider the long time behavior of solution for the Benjamin-Bona-Mahony equations with periodic boundary conditions. By the method of orthogonal decomposition, we show that the existence of asymptotic attractor which overcome difficulty come from the precision of approximate inertial manifolds. Moreover, the dimensions estimate of the asymptotic attractor is obtained.