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.
Corsi, L., Montalto, R. (2018). Quasi-periodic solutions for the forced Kirchhoff equation on $T^d$. NONLINEARITY, 31(11), 5075-5109 [10.1088/1361-6544/aad6fe].
Quasi-periodic solutions for the forced Kirchhoff equation on $T^d$
Corsi, Livia;Montalto, Riccardo
2018-01-01
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.| File | Dimensione | Formato | |
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