Attractors for Semigroups and Evolution Equations

Olga A. Ladyzhenskaya, Gregory A. Seregin, Varga K. Kalantarov (Koc University, Istanbul) , Sergey V. Zelik (University of Surrey)

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English

Cambridge University Press
09 June 2022

Differential calculus & equations; Dynamics & statics

Series: Cambridge Mathematical Library

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.

By: Olga A. Ladyzhenskaya
Foreword by: Gregory A. Seregin, Varga K. Kalantarov (Koc University, Istanbul), Sergey V. Zelik (University of Surrey)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: Revised edition
Dimensions: Height: 228mm, Width: 151mm, Spine: 6mm
Weight: 164g
ISBN: 9781009229821
ISBN 10: 1009229826
Series: Cambridge Mathematical Library
Pages: 115
Publication Date: 09 June 2022
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

Part I. Attractors for the Semigroups of Operators: 1. Basic notions; 2. Semigroups of class K; 3. Semigroups of class AK; 4. On dimensions of compact invariant sets; Part II: Semigroups Generated by Evolution Equations: 5. Introduction to Part II; 6. Estimates for the number of determining modes and the fractal dimension of bounded invariant sets for the Navier-Stokes equations; 7. Evolution equations of hyperbolic type; References; Index.

Olga A. Ladyzhenskaya was a prolific Russian mathematician most well known for her work on partial differential equations and fluid mechanics. She authored over 200 hundred research works and became Head of the Mathematical Physics Laboratory of the Steklov Institute in 1961. Her many accolades include giving the Emmy Noether lecture at the International Congress of Mathematicians in 1994; giving the von Neumann lecture, the highest distinction of the Society for Industrial and Applied Mathematics, in 1998; and the Lomonosov Gold Medal, the highest award of the Russian Academy of Sciences, in 2002. Gregory A. Seregin is Emeritus Professor of Mathematics at the University of Oxford. Varga K. Kalantarov is Professor of Mathematics at Koc University. Sergey V. Zelik is Professor of Mathematics at the University of Surrey.

Reviews for Attractors for Semigroups and Evolution Equations

'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