Abstract
Our aim here and the next two chapters is to prove two important properties of the inertial manifolds that are not (usually) satisfied by the attractors. In this chapter and Chapter 13 the property that we prove is the asymptotic completeness of the inertial manifold \(\bar \sum \) that we have constructed. We recall that the asymptotic completeness means that given any orbit of the dynamical system, we can find another orbit lying on \(\bar \sum \) that produces the same limit behavior at t → ∞.
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© 1989 Springer-Verlag New York Inc.
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Constantin, P., Foias, C., Nicolaenko, B., Teman, R. (1989). Asymptotic Completeness: Preparation. In: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Applied Mathematical Sciences, vol 70. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3506-4_13
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DOI: https://doi.org/10.1007/978-1-4612-3506-4_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8131-3
Online ISBN: 978-1-4612-3506-4
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