Advances in Differential Equations

Exponential averaging under rapid quasiperiodic forcing

Karsten Matthies

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 Simó, Galerkin approximations and high regularity of the initial conditions. Similar finite order estimates assuming less regularity are also provided. Examples include reaction-diffusion and non-linear Schrödinger equations.

Article information

Source
Adv. Differential Equations Volume 13, Number 5-6 (2008), 427-456.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867341

Mathematical Reviews number (MathSciNet)
MR2482394

Zentralblatt MATH identifier
1154.37371

Subjects
Primary: 34C29: Averaging method
Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 35A35: Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx} 35K57: Reaction-diffusion equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 37J40: Perturbations, normal forms, small divisors, KAM theory, Arnol d diffusion

Citation

Matthies, Karsten. Exponential averaging under rapid quasiperiodic forcing. Adv. Differential Equations 13 (2008), no. 5-6, 427--456.https://projecteuclid.org/euclid.ade/1355867341


Export citation