Propose de développer une méthode de formes normales de Birkhoff appliquée aux équations quasi linéraires de Klein-Gordon sur S1 ; afin d'étendre ce résultat à des non-linéarités quasi-linéaires hamiltoniennes générales. ©Electre 2025
Consider a nonlinear Klein-Gordon equation on the unit circle, with smooth data of size (...). A solution u which, for any (...), may be extended as a smooth solution on a time-interval (...) for some Ck > 0 and for (...), is called an almost global solution. It is known that when the nonlinearity is a polynomial depending only on u, and vanishing at order at least 2 at the origin, any smooth small Cauchy data generate, as soon as the mass parameter in the equation stays outside a subset of zero measure of (...)+, an almost global solution, whose Sobolev norms of higher order stay uniformly bounded. The goal of this paper is to extend this result to general Hamiltonian quasi-linear nonlinearities. These are the only Hamiltonian non linearities that depend not only on u, but also on its space derivative. To prove the main theorem, we develop a Birkhoff normal form method for quasi-linear equations.
Paru le : 30/01/2012
Thématique : Physique générale
Auteur(s) : Auteur : Jean-Marc Delort
Éditeur(s) :
Société mathématique de France
Collection(s) : Non précisé.
Série(s) : Non précisé.
ISBN : 978-2-85629-335-5
EAN13 : 9782856293355
Reliure : Broché
Pages : 112
Hauteur: 24.0 cm / Largeur 18.0 cm
Poids: 0 g
Carte fidélité
Mollat Radio
