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Steady Approximate Inertial Manifolds of Exponential Order for Semilinear Parabolic Equations

The long time behavior of a class of autonomous semilinear parabolic equations is investigated. We employ the recently introduced concept of Inertial Manifold with Delay to construct a new family of approximate inertial manifolds (AIM) of an exponential order. These AIMs contain all steady states of the system under consideration.