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Attractors. Then and now

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arxiv 2208.12101 v1 pith:7MNWZEDP submitted 2022-08-25 math.DS math.AP

Sergey Zelik This is my paper · ORCID
classification math.DSmath.AP
keywords attractorsnumberresultstheoryuniversityaboveanniversaryauthor
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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 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 above mentioned classes of attractors. The theoretical results are illustrated by a number of clarifying examples and counter-examples.

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Cited by 2 Pith papers

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  2. Non-autonomous problem for a $2m$-th order semilinear nonlocal parabolic equation

    math.AP 2025-07 reject novelty 4.0 of 10

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