Attractors. Then and now

Abstract

This survey is dedicated to the 100th anniversary of Mark Iosifovich Vishik and is based on a number of mini-courses taught by the author at the University of Surrey (UK) and Lanzhou University (China). It discusses the classical and modern results of the theory of attractors for dissipative PDEs, including attractors for autonomous and non-autonomous equations, dynamical systems in general topological spaces, various types of trajectory, pullback and random attractors, exponential attractors, determining functionals and inertial manifolds, as well as the dimension theory for the classes of attractors mentioned above. The theoretical results are illustrated by a number of clarifying examples and counterexamples. Bibliography: 248 titles.