Quasi-periodic solutions for the forced Kirchhoff equation on $\mathbb{T}^d$
Analysis of PDEs
2018-11-14 v1
Abstract
In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the -dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a quasi-linear equations in high dimension. The proof is based on a Nash-Moser scheme in Sobolev class and a regularization procedure combined with a multiscale analysis in order to solve the linearized problem at any approximate solution.
Keywords
Cite
@article{arxiv.1802.04139,
title = {Quasi-periodic solutions for the forced Kirchhoff equation on $\mathbb{T}^d$},
author = {Livia Corsi and Riccardo Montalto},
journal= {arXiv preprint arXiv:1802.04139},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1311.6943