Attractors. Then and now

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Abstract

This survey is dedicated to the 100th anniversary of Mark Iosifovich Vishikand is based on a number of mini-courses taught by the author at the Universityof Surrey (UK) and Lanzhou University (China). It discusses the classicaland 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 theoryfor the classes of attractors mentioned above. The theoretical resultsare illustrated by a number of clarifying examples and counterexamples.Bibliography: 248 titles.

About the authors

Sergey Vital'evich Zelik

Zhejiang Normal University; University of Surrey; Keldysh Institute of Applied Mathematics of Russian Academy of Sciences

Email: s.zelik@surrey.ac.uk
Doctor of physico-mathematical sciences, Senior Researcher

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