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In this article we introduce two new generalizations of inertial manifolds. The first
one is the concept of Inertial Manifold with Delay which may be
physically more suitable than
the usual concept of inertial manifold since it allows
a certain delay time for the adjustment
of the small scales to the large ones. We also introduce an
invariant manifold which is
the graph of a multivalued function and which exists
under general conditions.
We conjecture that, like an inertial manifold, this manifold
attracts all orbits at an exponential rate.