论文标题
吸引者。然后现在
Attractors. Then and now
论文作者
论文摘要
这项调查专门纪念马克·艾西福维奇·维希克（Mark Iosifovich Vishik）成立100周年，并基于作者在英国萨里大学（University of Surrey）（英国）和兰州大学（Lanzhou University）（中国）教授的许多迷你演奏。它讨论了耗散PDE的吸引者理论的经典和现代结果，包括自主和非自主方程的吸引子，一般拓扑空间中的动态系统，各种类型的轨迹，回溯和随机吸引子，指数吸引子，确定功能和惯性流形以及上述吸引者的维度理论以及吸引者的维度理论。理论结果通过许多澄清的例子和反例来说明。
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.
