Attractors and Approximate Inertial Manifolds for the Generalized Benjamin-Bona-Mahony Equation

Abstract

In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in H k for every integer k ≥ 2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time.