Titlebook: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations; P. Constantin,C. Foias,R. Teman Book 1989 Spring

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Spectral Blocking Property,Our aim is to investigate the time evolution of the position of Ker(. − .(.)) relative to the fixed system of coordinates given by . .,… .,… (the eigenvectors of .).

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Strong Squeezing Property,Let .,(.) = .(.)., . = 1, 2, be two solutions of (2.1). Then their difference . = .(.) − .(.) satisfies the equation . where ..

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Cone Invariance Properties,One of the features of a dissipative equation of type (2.1), (2.2) is the existence of compact absorbing sets. More precisely, there exists . ⊂ . satisfying

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Consequences Regarding the Global Attractor,Let . be the global attractor of the dissipative system under consideration. Recall that . is the largest set in . with the properties

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Choice of the Initial Manifold,We are now going to describe the set of initial data for our integral manifold. In order to make our treatment more transparent we shall assume that

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