UNIGE document Scientific Article
previous document  unige:21873  next document
add to browser collection
Title

Metastable energy strata in weakly nonlinear wave equations

Authors
Gauckler, Ludwig
Lubich, Christian
Weiss, Daniel
Published in Communications in Partial Differential Equations. 2012, vol. 37, no. 8, p. 1391-1413
Abstract We consider the problem of the long-time stability of plane waves under nonlinear perturbations of linear Klein-Gordon equations. This problem reduces to studying the distribution of the mode energies along solutions of one-dimensional semilinear Klein-Gordon equations with periodic boundary conditions when the initial data are small and concentrated in one Fourier mode. It is shown that for all except finitely many values of the mass parameter, the energy remains essentially localized in the initial Fourier mode over time scales that are much longer than predicted by standard perturbation theory. The mode energies decay geometrically with the mode number with a rate that is proportional to the total energy. The result is proved using modulated Fourier expansions in time.
Keywords Nonlinear wave equationModulated Fourier expansionMode energies
Identifiers
Full text
Structures
Citation
(ISO format)
GAUCKLER, Ludwig et al. Metastable energy strata in weakly nonlinear wave equations. In: Communications in Partial Differential Equations, 2012, vol. 37, n° 8, p. 1391-1413. https://archive-ouverte.unige.ch/unige:21873

159 hits

86 downloads

Update

Deposited on : 2012-07-18

Export document
Format :
Citation style :