Attractors for Semigroups and Evolution Equations

Olga A. Ladyzhenskaya; Gregory A. Seregin; Varga K. Kalantarov; Sergey V. Zelik

doi:10.1017/9781009229814

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Zelik, Sergey Vital'evich 2023. Attractors. Then and now. Russian Mathematical Surveys, Vol. 78, Issue. 4, p. 635.

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Zelik, Sergey Vital'evich 2023. Attractors. Then and now. Успехи математических наук, Vol. 78, Issue. 4(472), p. 53.

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Zhou, Quan Liu, Yang and Yang, Dong 2024. Global attractors for a class of viscoelastic plate equations with past history. AIMS Mathematics, Vol. 9, Issue. 9, p. 24887.

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Mao, Rongyan Liu, Hui Miao, Fahe and Xin, Jie 2024. Global Attractors for the Three-Dimensional Tropical Climate Model with Damping Terms. Bulletin of the Malaysian Mathematical Sciences Society, Vol. 47, Issue. 2,

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Olga A. Ladyzhenskaya
Foreword by Gregory A. Seregin, Steklov Institute of Mathematics, St Petersburg and University of Oxford, Varga K. Kalantarov, Koç University, Istanbul, Sergey V. Zelik, University of Surrey

Publisher:: Cambridge University Press
Online publication date:: May 2022
Print publication year:: 2022
Online ISBN:: 9781009229814
DOI:: https://doi.org/10.1017/9781009229814

Subjects:: Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Fluid Dynamics and Solid Mechanics
Series:: Cambridge Mathematical Library

19.99 (GBP)

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In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.

‘This booklet is a personal essay summarizing Ladyzhenskaya’s views and her results. … Ladyzhenskaya has been a leading scholar in this area; she is a star and one should pay attention to what she says.’

Jerome A. Goldstein - SIAM Review

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Attractors for Semigroups and Evolution Equations

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-xxvi

Preface
pp xxvii-xxviii

Part I - Attractors for the Semigroups of Operators: An Abstract Framework
pp 1-2

1 - Basic notions
pp 3-5

2 - Semigroups of class K
pp 6-10

3 - Semigroups of class AK
pp 11-13

Afterword
pp 14-14

4 - On dimensions of compact invariant sets
pp 15-30

Part II - Semigroups Generated by Evolution Equations
pp 31-32

5 - Introduction to Part II
pp 33-34

6 - Estimates for the number of determining modes and the fractal dimension of bounded invariant sets for the Navier–Stokes equations
pp 35-38

7 - Evolution equations of hyperbolic type
pp 39-65

References
pp 66-67

Index
pp 68-68

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