Attractors for infinitedimensional nonautonomous dynamical systems
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The work Attractors for infinitedimensional nonautonomous dynamical systems represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Attractors for infinitedimensional nonautonomous dynamical systems
Resource Information
The work Attractors for infinitedimensional nonautonomous dynamical systems represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Attractors for infinitedimensional nonautonomous dynamical systems
 Statement of responsibility
 Alexandre N. Carvalho, José A. Langa, James C. Robinson
 Subject

 Attractors (Mathematics)
 Attractors (Mathematics)
 Cell aggregation  Mathematics.
 Differentiable dynamical systems.
 Differential equations, partial.
 Dynamical Systems and Ergodic Theory.
 MATHEMATICS  Calculus
 MATHEMATICS  Mathematical Analysis
 Manifolds and Cell Complexes (incl. Diff. Topology)
 Mathematics
 Mathematics.
 Partial Differential Equations.
 Attractors (Mathematics)
 Language
 eng
 Summary
 This book treats the theory of pullback attractors for nonautonomous dynamical systems. While the emphasis is on infinitedimensional systems, the results are also applied to a variety of finitedimensional examples. The purpose of the book is to provide a summary of the current theory, starting with basic definitions and proceeding all the way to stateoftheart results. As such it is intended as a primer for graduate students, and a reference for more established researchers in the field. The basic topics are existence results for pullback attractors, their continuity under perturbation, techniques for showing that their fibres are finitedimensional, and structural results for pullback attractors for small nonautonomous perturbations of gradient systems (those with a Lyapunov function). The structural results stem from a dynamical characterisation of autonomous gradient systems, which shows in particular that such systems are stable under perturbation. Application of the structural results relies on the continuity of unstable manifolds under perturbation, which in turn is based on the robustness of exponential dichotomies: a selfcontained development of these topics is given in full. After providing all the necessary theory the book treats a number of model problems in detail, demonstrating the wide applicability of the definitions and techniques introduced: these include a simple LotkaVolterra ordinary differential equation, delay differential equations, the twodimensional NavierStokes equations, general reactiondiffusion problems, a nonautonomous version of the ChafeeInfante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a nonautonomous damped wave equation. Alexandre N. Carvalho is a Professor at the University of Sao Paulo, Brazil. José A. Langa is a Profesor Titular at the University of Seville, Spain. James C. Robinson is a Professor at the University of Warwick, UK
 Cataloging source
 GW5XE
 Dewey number
 515/.39
 Index
 index present
 Language note
 English
 LC call number
 QA614.813
 LC item number
 .C37 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Applied mathematical sciences,
 Series volume
 v. 182
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Context of Attractors for infinitedimensional nonautonomous dynamical systemsWork of
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