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From the Newton equation to the wave equation in some simple cases

Blanc, Xavier; Le Bris, Claude; Lions, Pierre-Louis (2012), From the Newton equation to the wave equation in some simple cases, Networks and Heterogeneous Media, 7, 1, p. 1-41. http://dx.doi.org/10.3934/nhm.2012.7.1

Type
Article accepté pour publication ou publié
Date
2012
Nom de la revue
Networks and Heterogeneous Media
Volume
7
Numéro
1
Éditeur
AIMS
Pages
1-41
Identifiant publication
Métadonnées
Afficher la notice complète
Auteur(s)
Blanc, Xavier cc
Le Bris, Claude
Lions, Pierre-Louis
Résumé (EN)
We prove that, in some simple situations at least, the one-dimensional wave equation is the limit as the microscopic scale goes to zero of some time-dependent Newton type equation of motion for atomistic systems. We address both some linear and some nonlinear cases.
Mots-clés
Macroscopic limit; Newton equation; nonlinear wave equation