Almost-periodic Response Solutions for a forced quasi-linear Airy equation
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 ${\mathbb T}^\infty$.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2020
- DOI:
- 10.48550/arXiv.2006.00313
- arXiv:
- arXiv:2006.00313
- Bibcode:
- 2020arXiv200600313C
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematics - Dynamical Systems;
- 37K55;
- 58C15;
- 35Q53;
- 35B15