Abstract
Precise estimates for the validity of the amplitude approximation for the swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of orderO(ɛ) which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of orderO(ɛ-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.
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Communicated by A. Jaffe
Dedicated to Res Jost and Arthur Wightman
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Collet, P., Eckmann, J.P. The time dependent amplitude equation for the Swift-Hohenberg problem. Commun.Math. Phys. 132, 139–153 (1990). https://doi.org/10.1007/BF02278004
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DOI: https://doi.org/10.1007/BF02278004