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A sharp condition for existence of an inertial manifold. (English) Zbl 0727.34048

Author’s abstract: “It is shown that a perturbation argument that guarantees persistence of inertial (invariant and exponentially attracting) manifolds for linear perturbations of linear evolution equations applied also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semilinear parabolic as well as for some nonlinear hyperbolic equations. Fourier transform of the explicitly given equation for the tracking solution together with the Plancherel’s theorem for Banach valued functions are used.”
Reviewer: J.Andres (Olomouc)

MSC:

34D45 Attractors of solutions to ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35L10 Second-order hyperbolic equations
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References:

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