Attractors for infinite-dimensional non-autonomous dynamical systems

This treatment of pull-back attractors for non-autonomous Dynamical systems emphasizes the infinite-dimensional variety but also analyzes those that are finite. As a graduate primer, it covers everything from basic definitions to cutting-edge results.

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.

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.-