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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.

Semigroups of operators. --- Evolution equations. --- Attractors (Mathematics)

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Semigroups of operators --- Evolution equations --- Attractors (Mathematics) --- Semigroups of operators. --- Evolution equations. --- Attractors (mathematics)

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The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete ch

Attractors (Mathematics) --- Chaotic behavior in systems --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems

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This book introduces complete and systematic theories of infinite-dimensional dynamical systems and their applications in partial differential equations, especially in the models of fluid mechanics. It is based on the first author’s lecture “Infinite dimensional dynamical systems on nonlinear autonomous systems” given to graduate students in Donghua University since 2004. This book presents recent results that have been carried out by the authors on autonomous nonlinear evolutionar yequations arising from physics, fluid mechanics and material science such as the Navier–Stokes equations, Navier–Stokes–Voight systems, the nonlinear thermoviscoelastic system, etc.

Functions of complex variables. --- Attractors (Mathematics) --- Nonlinear systems.

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The study of dissipative equations is an area that has attracted substantial attention over many years. Much progress has been achieved using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field.

Attractors (Mathematics) --- Differential equations, Parabolic. --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems --- Differential equations, Parabolic