CONTINUUM LIMIT OF THE DISCRETE NONLINEAR KLEIN-GORDON EQUATION

Chauleur, Quentin

Document type :

Pré-publication ou Document de travail

Title :

CONTINUUM LIMIT OF THE DISCRETE NONLINEAR KLEIN-GORDON EQUATION

Author(s) :

Chauleur, Quentin [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Systèmes de particules et systèmes dynamiques [Paradyse]

English keyword(s) :

Growth of Sobolev Norms
Continuum limit
Nonlinear wave and Klein-Gordon equations

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. ...
Show more >We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies in particular on the use of bilinear estimates of the Shannon interpolation alongside controls on the growth of discrete Sobolev norms of the solution. We conclude by giving perspectives on uniform dispersive estimates for nonlinear waves on lattices.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :