Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions

被引：43

作者：

Cohen, David ^{[1
]}

Hairer, Ernst ^{[2
]}

Lubich, Christian ^{[3
]}

机构：

[1] Univ Basel, Math Inst, CH-4051 Basel, Switzerland

[2] Univ Geneva, Dept Math, CH-1211 Geneva 4, Switzerland

[3] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2008年 / 187卷 / 02期

关键词：

D O I：

10.1007/s00205-007-0095-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：341 / 368

页数：28

共 16 条

[1] Birkhoff normal form for partial differential equations with tame modulus [J].