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∞.
Almost-periodic solutions for PDEs; KdV; Nash–Moser-KAM theory; Small divisor problems
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/850608
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