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Attractors for Semigroups and Evolution Equations

Part of Cambridge Mathematical Library

  • Date Published: June 2022
  • availability: Available
  • format: Paperback
  • isbn: 9781009229821

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About the Authors
  • 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.

    • Ladyzhenskaya's survey of her own work on partial differential equations and dynamical systems
    • Contains a new technical introduction written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik
    • Shines a light on the often-overlooked results of Soviet mathematicians working in this area
    Read more

    Reviews & endorsements

    '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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    Product details

    • Date Published: June 2022
    • format: Paperback
    • isbn: 9781009229821
    • length: 115 pages
    • dimensions: 229 x 152 x 6 mm
    • weight: 0.156kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    Olga A. Ladyzhenskaya
    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.

    Foreword

    Gregory A. Seregin, Steklov Institute of Mathematics, St Petersburg and University of Oxford
    Gregory A. Seregin is Emeritus Professor of Mathematics at the University of Oxford.

    Varga K. Kalantarov, Koç University, Istanbul
    Varga K. Kalantarov is Professor of Mathematics at Koç University.

    Sergey V. Zelik, University of Surrey
    Sergey V. Zelik is Professor of Mathematics at the University of Surrey.

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