Attractors for Semigroups and Evolution Equations

Ladyzhenskaya's survey of her work on partial differential equations and dynamical systems, with a new technical introduction.

Olga A. Ladyzhenskaya (Author), Gregory A. Seregin (Foreword by), Varga K. Kalantarov (Foreword by), Sergey V. Zelik (Foreword by)

9781009229821, Cambridge University Press

Paperback / softback, published 9 June 2022

115 pages
22.8 x 15.1 x 0.6 cm, 0.164 kg

'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

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.

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.

Subject Areas: Dynamics & statics [PHDT], Differential calculus & equations [PBKJ]