Attractors for infinite-dimensional non-autonomous dynamical systems

2013
ISBN: 978-1-4899-9176-8
Verlag: Springer

Buch, Englisch, Band 182, 412 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 674 g

Reihe: Applied Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Carvalho, Alexandre

Robinson, James

Langa, José A.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

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.-

Über Autor(innen)

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.