Spectral semi-discretisations of weakly non-linear wave equations over long times (Q941795)
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scientific article; zbMATH DE number 5319279
| Language | Label | Description | Also known as |
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| English | Spectral semi-discretisations of weakly non-linear wave equations over long times |
scientific article; zbMATH DE number 5319279 |
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Spectral semi-discretisations of weakly non-linear wave equations over long times (English)
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2 September 2008
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The authors consider the one-dimensional wave equation along with a weak non-linearity, with periodic boundary conditions and small initial values, and prove near conservation over long time intervals of harmonic actions, energy and momentum (the latter not being conserved exactly) of its semi-discrete solutions. This is done using the modulated Fourier expansion and heavily referring to an earlier paper by the \textit{D. Cohen} and the authors [see Arch. Ration. Mech. Anal. 187, No.~2, 341--368 (2008; Zbl 1145.35087)].
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long-time behaviour
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regularity of solutions
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near conservation of harmonic actions
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energy and momentum
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modulated Fourier expansion
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periodic boundary conditions
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