Quasi-periodic solutions of PDEs

Massimiliano Berti[1]

  • [1] Dipartimento di Matematica e Applicazioni “R. Caccioppoli" Università degli Studi Napoli Federico II Via Cintia, Monte S. Angelo I-80126, Napoli Italy

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • Volume: 2011-2012, page 1-11
  • ISSN: 2266-0607

Abstract

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The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in 𝕋 d , d ≥ 2 , and the 1 - d derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.

How to cite

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Berti, Massimiliano. "Quasi-periodic solutions of PDEs." Séminaire Laurent Schwartz — EDP et applications 2011-2012 (2011-2012): 1-11. <http://eudml.org/doc/251155>.

@article{Berti2011-2012,
abstract = {The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in $ \mathbb\{T\}^d $, $ d \ge 2 $, and the $1$-$d$ derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.},
affiliation = {Dipartimento di Matematica e Applicazioni “R. Caccioppoli" Università degli Studi Napoli Federico II Via Cintia, Monte S. Angelo I-80126, Napoli Italy},
author = {Berti, Massimiliano},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {KAM for PDE; Nash-Moser theory; quasi-periodic solutions; small divisors; nonlinear Schrödinger and wave equation; infinite dimensional Hamiltonian systems},
language = {eng},
pages = {1-11},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Quasi-periodic solutions of PDEs},
url = {http://eudml.org/doc/251155},
volume = {2011-2012},
year = {2011-2012},
}

TY - JOUR
AU - Berti, Massimiliano
TI - Quasi-periodic solutions of PDEs
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2011-2012
SP - 1
EP - 11
AB - The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in $ \mathbb{T}^d $, $ d \ge 2 $, and the $1$-$d$ derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
LA - eng
KW - KAM for PDE; Nash-Moser theory; quasi-periodic solutions; small divisors; nonlinear Schrödinger and wave equation; infinite dimensional Hamiltonian systems
UR - http://eudml.org/doc/251155
ER -

References

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