This article is cited in 15 papers

Attractors. Then and now

S. V. Zelik<sup>abc

a</sup> Zhejiang Normal University, Department of Mathematics, Zhejiang, P. R. China
^b University of Surrey, Department of Mathematics, Guildford, United Kingdom
^c Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia

Abstract: This survey 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.

Keywords: dissipative PDEs, attractors, inertial manifolds, determining functionals, finite-dimensional reduction.

MSC: 35B41, 37L30

Received: 25.08.2022

Language: English

DOI: 10.4213/rm10095

 English version: Russian Mathematical Surveys, 2023, 78:4, 635–777

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