Some new generalizations of inertial manifolds. (English) Zbl 0948.35018

Debussche, A.; Temam, R.

Discrete Contin. Dyn. Syst. 2, No. 4, 543-558 (1996).

Summary: 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.

MSC:

35B42	Inertial manifolds
47J35	Nonlinear evolution equations
35K90	Abstract parabolic equations

Keywords:

inertial manifold with delay; invariant manifold which is the graph of a multivalued function