Geodesic
Attractors. Then and now
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 4, pp. 635-777

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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: attractors, inertial manifolds, determining functionals, finite-dimensional reduction.
Mots-clés : dissipative PDEs 
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S. V. Zelik. Attractors. Then and now. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 78 (2023) no. 4, pp. 635-777. http://geodesic.mathdoc.fr/item/RM_2023_78_4_a1/