C1Approximations of Inertial Manifolds for Dissipative Nonlinear Equations

Abstract

In this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds. This means that the long-time behavior is equivalent to a certain finite system of ordinary differential equations. We investigate ways in which these finite systems can be approximated in theC1sense. Geometrically this may be interpreted as constructing manifolds in phase space that areC1close to the inertial manifold of the partial differential equation. Under such approximations the invariant hyperbolic sets of the global attractor persist.