Quasi- periodic solutions for the forced Kirchhoff equation on Td

被引：20

作者：

Corsi, Livia ^{[1
]}

Montalto, Riccardo ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, 686 Cherry St NW, Atlanta, GA 30332 USA

[2] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

来源：

NONLINEARITY | 2018年 / 31卷 / 11期

基金：

瑞士国家科学基金会;

关键词：

Kirchhoff equation; quasi-linear PDEs; quasi-periodic solutions; infinite-dimensional dynamical systems; Nash-Moser theory; PARTIAL-DIFFERENTIAL-EQUATIONS; NONLINEAR-WAVE EQUATIONS; SCHRODINGER-EQUATIONS; KAM; PERTURBATIONS; THEOREM; SINGULARITIES; KDV; NLS;

D O I：

10.1088/1361-6544/aad6fe

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the existence of small-amplitude quasi-periodic solutions with Sobolev regularity, for the d-dimensional forced Kirchhoff equation with periodic boundary conditions. This is the first result of this type for a quasi-linear equation 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.

引用

页码：5075 / 5109

页数：35

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