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Luskin, Mitchell; Sell, George R.

Approximation theories for inertial manifolds. (English) Zbl 0688.58035

RAIRO, Modélisation Math. Anal. Numér. 23, No. 3, 445-461 (1989).
This paper presents a brief review of the existence theories for inertial manifolds via Lyapunov-Perron method, the Hadamard graph transform method and the method of elliptic or parabolic regularization, and three methods for approximating inertial manifolds which can be viewed as modified Galerkin approximation. The advantages and faults of various existence theories of inertial manifolds are discussed from the viewpoint of numerical approximation.
Reviewer: J.Wu

Cited in 15 Documents

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
35K57 Reaction-diffusion equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

inertial manifolds; Lyapunov-Perron method; modified Galerkin approximation
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\textit{M. Luskin} and \textit{G. R. Sell}, RAIRO, Modélisation Math. Anal. Numér. 23, No. 3, 445--461 (1989; Zbl 0688.58035)
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References:

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