Abstract
We consider two dissipative systems having inertial manifolds and give estimates which allow us to compare the flows on the two inertial manifolds. As an example of a modulated system we treat the Swift–Hohenberg equation , ∈ ℝ, with periodic boundary conditions on the interval . Recent results in the theory of modulation equation show that the solutions of this equation can be described over long time scales by those of the associated Ginzburg–Landau equation ∈ ℂ, with suitably generalized periodic boundary conditions on . We prove that both systems have an inertial manifold of the same dimension and that the flows on these finite dimensional manifolds converge against each other for .
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