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
Quasi-periodic solutions for the forced Kirchhoff equation on T^d / L. Corsi, R. Montalto. - In: NONLINEARITY. - ISSN 0951-7715. - 31:11(2018 Oct 10), pp. 5075-5109. [10.1088/1361-6544/aad6fe]
Quasi-periodic solutions for the forced Kirchhoff equation on T^d
R. Montalto
2018
Abstract
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
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Corsi_2018_Nonlinearity_31_5075.pdf
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