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∞.
Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation / L. Corsi, R. Montalto, M. Procesi. - In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. - ISSN 1040-7294. - (2020 Oct 23). [Epub ahead of print]
Almost-Periodic Response Solutions for a Forced Quasi-Linear Airy Equation
R. Montalto
;
2020
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∞.
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