Overview

The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.

Full Product Details

Author:   Alexandre Carvalho ,  José A. Langa ,  James Robinson
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2013 ed.
Volume:   182
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   0.682kg
ISBN:  

9781489991768

ISBN 10:   148999176
Pages:   412
Publication Date:   15 October 2014
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

The pullback attractor.- Existence results for pullback attractors.- Continuity of attractors.- Finite-dimensional attractors.- Gradient semigroups and their dynamical properties.- Semilinear Differential Equations.- Exponential dichotomies.- Hyperbolic solutions and their stable and unstable manifolds.- A non-autonomous competitive Lotka-Volterra system.- Delay differential equations.-The Navier–Stokes equations with non-autonomous forcing.-  Applications to parabolic problems.- A non-autonomous Chafee–Infante equation.- Perturbation of diffusion and continuity of attractors with rate.- A non-autonomous damped wave equation.- References.- Index.-

Reviews

From the reviews: The Carvalho, Langa and Robinson monograph focuses primarily on infinite-dimensional systems and evolution equations. ... The monograph is suitable for graduate students with a background on functional analysis and evolution equations. ... Carvalho, Langa and Robinson present a readable and thorough account of the current state of the theory, which provides the reader with ready access to an area that has considerable potential for further development. (Peter E. Kloeden, Mathematical Reviews, July, 2013) This monograph not only summarizes the research of the authors over the last decade, but also provides an accessible and well-written approach to the recent theory of non-autonomous dynamical systems in infinite dimensions with a focus on corresponding attractors and invariant manifolds. ... This book is a well-written and carefully prepared text appropriate for advanced classes on dynamical systems and seminars. (Christian Potzsche, Zentralblatt MATH, Vol. 1263, 2013)

Author Information

Alexandre N. Carvalho is a Professor at University of Sao Paulo, Brazil. José A. Langa is a Professor at University of Seville, Spain. James C. Robinson is a Professor at University of Warwick, UK.

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