Quasi-periodic solutions for 1D resonant beam equation

Zhenguo Liang; Jiansheng Geng

doi:10.3934/cpaa.2006.5.839

Article Contents

2006, Volume 5, Issue 4: 839-853. Doi: 10.3934/cpaa.2006.5.839

This issue Previous Article Convergence to stationary solutions for a parabolic-hyperbolic phase-field system Next Article A Liouville type Theorem for an integral system

Quasi-periodic solutions for 1D resonant beam equation

Zhenguo Liang^1, and
Jiansheng Geng^2,

1.
School of Mathematical Sciences, Institute of Mathematics, Fudan University, Shanghai 200433
2.
Department of Mathematics, Nanjing University, Nanjing 210093

Received: December 31, 2005

Revised: May 31, 2006

Published: November 2006

Abstract Related Papers Cited by

Abstract

In this paper, one--dimensional ($1D$) resonant beam equation

$u_{t t} +u_{x x x x} +u^3=0,$

with hinged boundary conditions is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. The proof is based on infinite dimensional KAM theorem, partial normal form and scaling skills.

Keywords:

Mathematics Subject Classification: 37K55.

Citation:

Article Metrics

HTML views() PDF downloads(145) Cited by(0)

Quasi-periodic solutions for 1D resonant beam equation

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Quasi-periodic solutions for 1D resonant beam equation

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content