Coverart for item
The Resource Attractors for infinite-dimensional non-autonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson

Attractors for infinite-dimensional non-autonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson

Label
Attractors for infinite-dimensional non-autonomous dynamical systems
Title
Attractors for infinite-dimensional non-autonomous dynamical systems
Statement of responsibility
Alexandre N. Carvalho, José A. Langa, James C. Robinson
Creator
Contributor
Subject
Language
eng
Summary
This book treats the theory of pullback attractors for non-autonomous dynamical systems. While the emphasis is on infinite-dimensional systems, the results are also applied to a variety of finite-dimensional 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 state-of-the-art 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 finite-dimensional, and structural results for pullback attractors for small non-autonomous 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 self-contained 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 Lotka-Volterra ordinary differential equation, delay differential equations, the two-dimensional Navier-Stokes equations, general reaction-diffusion problems, a non-autonomous version of the Chafee-Infante problem, a comparison of attractors in problems with perturbations to the diffusion term, and a non-autonomous 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
Member of
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 infinite-dimensional non-autonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
Instantiates
Publication
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 non-autonomous competitive Lotka-Volterra system
  • Delay differential equations
  • The Navier-Stokes equations with non-autonomous forcing
  • Applications to parabolic problems
  • Part 1.
  • A non-autonomous Chafee-Infante equation
  • Perturbation of diffusion and continuity of global attractors with rate of convergence
  • A non-autonomous damped wave equation
  • Appendix: Skew-product flows and the uniform attractor
  • Abstract theory
  • The pullback attractor
  • Existence results for pullback attractors
  • Continuity of attractors
  • Finite-dimensional 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
10.1007/978-1-4614-4581-4
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 infinite-dimensional non-autonomous dynamical systems, Alexandre N. Carvalho, José A. Langa, James C. Robinson
Publication
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 non-autonomous competitive Lotka-Volterra system
  • Delay differential equations
  • The Navier-Stokes equations with non-autonomous forcing
  • Applications to parabolic problems
  • Part 1.
  • A non-autonomous Chafee-Infante equation
  • Perturbation of diffusion and continuity of global attractors with rate of convergence
  • A non-autonomous damped wave equation
  • Appendix: Skew-product flows and the uniform attractor
  • Abstract theory
  • The pullback attractor
  • Existence results for pullback attractors
  • Continuity of attractors
  • Finite-dimensional 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
10.1007/978-1-4614-4581-4
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

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