Attractors for Semigroups and Evolution Equations

✍ Scribed by Olga A. Ladyzhenskaya

• Publisher: Cambridge University Press
• Year: 2022
• Tongue: English
• Leaves: 97
• Series: Cambridge Mathematical Library
• Edition: Revised
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

01.0_pp_i_iv_Frontmatter
02.0_pp_v_vi_Contents
03.0_pp_vii_xxvi_Introduction
04.0_pp_xxvii_xxviii_Preface
05.0_pp_1_2_Attractors_for_the_Semigroups_of_Operators_An_Abstract_Framework
05.1_pp_3_5_Basic_notions
05.2_pp_6_10_Semigroups_of_class_K
05.3_pp_11_13_Semigroups_of_class_AK
05.4_pp_14_14_Afterword
05.5_pp_15_30_On_dimensions_of_compact_invariant_sets
06.0_pp_31_32_Semigroups_Generated_by_Evolution_Equations
06.1_pp_33_34_Introduction_to_Part_II
06.2_pp_35_38_Estimates_for_the_number_of_determining_modes_and_the_fractal_dimension_of_bounded_invariant_sets_fo
06.3_pp_39_65_Evolution_equations_of_hyperbolic_type
07.0_pp_66_67_References
08.0_pp_68_68_Index