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A sharp condition for existence of an inertial manifold

  • Milan Miklavčič
Article

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 applies also when the perturbation is nonlinear. This gives a simple but sharp condition for existence of inertial manifolds for semi-linear 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.

Key words

Inertial invariant exponentially attracting manifolds non-linear evolution equations 

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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Milan Miklavčič
    • 1
  1. 1.Department of MathematicsMichigan State UniversityEast Lansing

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