The Resource Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
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The item Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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
 Language
 eng
 Extent
 1 online resource.
 Contents

 Invariant manifolds of hyperbolic solutions
 Semilinear differential equations
 Exponential dichotomies
 Hyperbolic solutions and their stable and unstable manifolds
 Part 3.
 Applications
 A nonautonomous competitive LotkaVolterra system
 Delay differential equations
 The NavierStokes equations with nonautonomous forcing
 Applications to parabolic problems
 Part 1.
 A nonautonomous ChafeeInfante equation
 Perturbation of diffusion and continuity of global attractors with rate of convergence
 A nonautonomous damped wave equation
 Appendix: Skewproduct flows and the uniform attractor
 Abstract theory
 The pullback attractor
 Existence results for pullback attractors
 Continuity of attractors
 Finitedimensional attractors
 Gradient semigroups and their dynamical properties
 Part 2.
 Isbn
 9781461445814
 Label
 Attractors for infinitedimensional nonautonomous dynamical systems
 Title
 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
 http://library.link/vocab/creatorName
 Carvalho, Alexandre Nolasco de
 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
 http://library.link/vocab/relatedWorkOrContributorDate
 1969
 http://library.link/vocab/relatedWorkOrContributorName

 Langa, José A
 Robinson, James C.
 Series statement
 Applied mathematical sciences,
 Series volume
 v. 182
 http://library.link/vocab/subjectName

 Attractors (Mathematics)
 Mathematics
 MATHEMATICS
 MATHEMATICS
 Attractors (Mathematics)
 Label
 Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Invariant manifolds of hyperbolic solutions
 Semilinear differential equations
 Exponential dichotomies
 Hyperbolic solutions and their stable and unstable manifolds
 Part 3.
 Applications
 A nonautonomous competitive LotkaVolterra system
 Delay differential equations
 The NavierStokes equations with nonautonomous forcing
 Applications to parabolic problems
 Part 1.
 A nonautonomous ChafeeInfante equation
 Perturbation of diffusion and continuity of global attractors with rate of convergence
 A nonautonomous damped wave equation
 Appendix: Skewproduct flows and the uniform attractor
 Abstract theory
 The pullback attractor
 Existence results for pullback attractors
 Continuity of attractors
 Finitedimensional attractors
 Gradient semigroups and their dynamical properties
 Part 2.
 Control code
 812174833
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9781461445814
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461445814
 http://library.link/vocab/ext/overdrive/overdriveId
 1461445809
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)812174833
 Label
 Attractors for infinitedimensional nonautonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Invariant manifolds of hyperbolic solutions
 Semilinear differential equations
 Exponential dichotomies
 Hyperbolic solutions and their stable and unstable manifolds
 Part 3.
 Applications
 A nonautonomous competitive LotkaVolterra system
 Delay differential equations
 The NavierStokes equations with nonautonomous forcing
 Applications to parabolic problems
 Part 1.
 A nonautonomous ChafeeInfante equation
 Perturbation of diffusion and continuity of global attractors with rate of convergence
 A nonautonomous damped wave equation
 Appendix: Skewproduct flows and the uniform attractor
 Abstract theory
 The pullback attractor
 Existence results for pullback attractors
 Continuity of attractors
 Finitedimensional attractors
 Gradient semigroups and their dynamical properties
 Part 2.
 Control code
 812174833
 Dimensions
 unknown
 Extent
 1 online resource.
 File format
 unknown
 Form of item
 online
 Isbn
 9781461445814
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9781461445814
 http://library.link/vocab/ext/overdrive/overdriveId
 1461445809
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)812174833
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)
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