Partial Inertial Manifolds for infinite-dimensional dynamical systems: Example for P.D.E.s with a state-dependent delay

Abstract

We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may exist in the cases when the classical Inertial manifold does not exist (or not known to exist).