Asymptotic Behavior of Dissipative Systems

by Hale, Jack K.

• ISBN13: 9780821849347
• ISBN10: 0821849344
• Format: Paperback
• Copyright: 2010-01-04
• Publisher: Amer Mathematical Society

Summary

Introduction Discrete dynamical systems: Limit sets Stability of invariant sets and asymptotically smooth maps Examples of asymptotically smooth maps Dissipativeness and global attractors Dependence on parameters Fixed point theorems Stability relative to the global attractor and Morse-Smale maps Dimension of the global attractor Dissipativeness in two spaces Notes and remarks Continuous dynamical systems: Limit sets Asymptotically smooth and $\alpha$-contracting semigroups Stability of invariant sets Dissipativeness and global attractors Dependence on parameters Periodic processes Skew product flows Gradient flows Dissipativeness in two spaces Properties of the flow on the global attractor Notes and remarks Applications: Retarded functional differential equations Sectorial evolutionary equations A scalar parabolic equation The Navier-Stokes equation Neutral functional differential equations Some abstract evolutionary equations A one-dimensional damped wave equation A three-dimensional damped wave equation Remarks on other applications Dependence on parameters and approximation of the attractor Appendix. Stable and unstable manifolds References Index

Table of Contents

Introduction

Discrete dynamical systems: Limit sets

Stability of invariant sets and asymptotically smooth maps

Examples of asymptotically smooth maps

Dissipativeness and global attractors

Dependence on parameters

Fixed point theorems

Stability relative to the global attractor and Morse-Smale maps

Dimension of the global attractor

Dissipativeness in two spaces

Notes and remarks

Continuous dynamical systems

Limit sets Asymptotically smooth and $\alpha$-contracting semigroups

Stability of invariant sets

Dissipativeness and global attractors

Dependence on parameters

Periodic processes Skew product flows

Gradient flows Dissipativeness in two spaces

Properties of the flow on the global attractor

Notes and remarks Applications: Retarded functional differential equations

Sectorial evolutionary equations

A scalar parabolic equation

The Navier-Stokes equation

Neutral functional differential equations

Some abstract evolutionary equations

A one-dimensional damped wave equation

A three-dimensional damped wave equation

Remarks on other applications

Dependence on parameters and approximation of the attractor

Appendix Stable and unstable manifolds

References

Index

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