A SHARP CONDITION FOR EXISTENCE OF AN INERTIAL MANIFOLD


Milan Miklavcic
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027

Published in Journal of Dynamics and Differential Equations 3(1991), 437-456.
(Also in IMA Preprint Series 604)



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 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.


Here is Introduction (in DVI format) and here is the whole paper in PDF format.

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