Abstract
A modulated Fourier expansion in time is used to show long-time near- conservation of the harmonic actions associated with spatial Fourier modes along the solutions of nonlinear wave equations with small initial data. The result implies the long-time near-preservation of the Sobolev-type norm that specifies the smallness condition on the initial data.
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Communicated by A. Mielke
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Cohen, D., Hairer, E. & Lubich, C. Long-Time Analysis of Nonlinearly Perturbed Wave Equations Via Modulated Fourier Expansions. Arch Rational Mech Anal 187, 341–368 (2008). https://doi.org/10.1007/s00205-007-0095-z
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DOI: https://doi.org/10.1007/s00205-007-0095-z