Approximation of Attractors and Inertial Manifolds. Convergent Families of Approximate Inertial Manifolds

Abstract

Our aim in this chapter is to study the approximation of attractors and inertial manifolds by smooth finite-dimensional manifolds, called approximate inertial manifolds. There is a vast and growing literature on approximation of attractors and inertial manifolds, approximate dynamics, and related algorithms. These important topics could justify, by themselves, the writing of one or several books; we will not try to give an exhaustive presentation or even an exhaustive bibliography on this question (see, however, a few references in Remark 3.2 at the end of this chapter).