Attractors for infinite-dimensional non-autonomous dynamical systems

✍ Scribed by Alexandre N. Carvalho, José A. Langa, James C. Robinson (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 433
• Series: Applied Mathematical Sciences 182
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xxxvi
Front Matter....Pages 1-1
The pullback attractor....Pages 3-22
Existence results for pullback attractors....Pages 23-53
Continuity of attractors....Pages 55-70
Finite-dimensional attractors....Pages 71-102
Gradient semigroups and their dynamical properties....Pages 103-139
Front Matter....Pages 141-141
Semilinear differential equations....Pages 143-186
Exponential dichotomies....Pages 187-222
Hyperbolic solutions and their stable and unstable manifolds....Pages 223-251
Front Matter....Pages 253-253
A non-autonomous competitive Lotka–Volterra system....Pages 255-263
Delay differential equations....Pages 265-279
The Navier–Stokes equations with non-autonomous forcing....Pages 281-300
Applications to parabolic problems....Pages 301-315
A non-autonomous Chafee–Infante equation....Pages 317-338
Perturbation of diffusion and continuity of global attractors with rate of convergence....Pages 339-359
A non-autonomous damped wave equation....Pages 361-376
Appendix: Skew-product flows and the uniform attractor....Pages 377-391
Back Matter....Pages 393-409

✦ Subjects

Partial Differential Equations; Dynamical Systems and Ergodic Theory; Manifolds and Cell Complexes (incl. Diff.Topology)