We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig–Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on T∞.
Corsi, L., Montalto, R., Procesi, M. (2021). Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS [10.1007/s10884-020-09906-8].
Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation
Corsi L.;Procesi M.
2021-01-01
Abstract
We prove the existence of almost-periodic solutions for quasi-linear perturbations of the Airy equation. This is the first result about the existence of this type of solutions for a quasi-linear PDE. The solutions turn out to be analytic in time and space. To prove our result we use a Craig–Wayne approach combined with a KAM reducibility scheme and pseudo-differential calculus on T∞.File in questo prodotto:
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