C-1 APPROXIMATIONS OF INERTIAL MANIFOLDS FOR DISSIPATIVE NONLINEAR EQUATIONS

In this paper we study a class of nonlinear dissipative partial differ ential equations that have inertial manifolds. This means that the lon g-time behavior is equivalent to a certain finite system of ordinary d ifferential equations. We investigate ways in which these finite syste ms can be approximated in the C-1 sense. Geometrically this may be int erpreted as constructing manifolds in phase space that are C-1 close t o the inertial manifold of the partial differential equation. Under su ch approximations the invariant hyperbolic sets of the global attracto r persist. (C) 1996 Academic Press, Inc.