### Abstract

We derive estimates on the magnitude of the interaction between a wide class of analytic
partial differential equations and a high-frequency quasiperiodic oscillator. Assuming high regularity
of initial conditions, the equations are transformed to an uncoupled system of an infinite
dimensional dynamical system and a linear quasiperiodic flow on a torus; up to coupling terms
which are exponentially small in the smallest frequency of the oscillator. The main technique is
based on a careful balance of similar results for ordinary differential equations by Sim´o, Galerkin
approximations and high regularity of the initial conditions. Similar finite order estimates assuming
less regularity are also provided. Examples include reaction-diffusion and nonlinear
Schr¨odinger equations.

Original language | English |
---|---|

Pages (from-to) | 427-456 |

Number of pages | 30 |

Journal | Advances in Differential Equations |

Volume | 13 |

Issue number | 5-6 |

Publication status | Published - 2008 |

## Fingerprint Dive into the research topics of 'Exponential averaging under rapid quasiperiodic forcing'. Together they form a unique fingerprint.

## Cite this

Matthies, K. (2008). Exponential averaging under rapid quasiperiodic forcing.

*Advances in Differential Equations*,*13*(5-6), 427-456.