Dynamics of Evolutionary Equations pp 569-592 | Cite as

# Inertial Manifolds: The Reduction Principle

Chapter

## Abstract

In the previous chapters, we have seen several illustrations of finite dimensional structures within the infinite dimensional dynamical systems. For example, many dissipative systems have global attractors, and oftentimes, the attractor A has finite Hausdorff and fractal dimensions. During the last few years it has been shown that some infinite dimensional nonlinear dissipative evolutionary equations have inertial manifolds. We will give the definition shortly.

## Keywords

Strong Solution Invariant Manifold Mild Solution Global Attractor Unique Fixed Point
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## Copyright information

© Springer Science+Business Media New York 2002