Perturbation problems in homogenization of hamilton-jacobi equations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2019

Perturbation problems in homogenization of hamilton-jacobi equations

Résumé

This paper is concerned with the behavior of the ergodic constant associated with convex and superlinear Hamilton-Jacobi equation in a periodic environment which is perturbed either by medium with increasing period or by a random Bernoulli perturbation with small parameter. We find a first order Taylor's expansion for the ergodic constant which depends on the dimension d. When d = 1 the first order term is non trivial, while for all d ≥ 2 it is always 0. Although such questions have been looked at in the context of linear uniformly elliptic homogenization, our results are the first of this kind in nonlinear settings. Our arguments, which rely on viscosity solutions and the weak KAM theory, also raise several new and challenging questions.
Fichier principal
Vignette du fichier
perturbations.pdf (340.72 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01435744 , version 1 (15-01-2017)

Identifiants

Citer

Pierre Cardaliaguet, Claude Le Bris, Panagiotis E Souganidis. Perturbation problems in homogenization of hamilton-jacobi equations. Journal de Mathématiques Pures et Appliquées, In press, 117, pp.221-262. ⟨10.1016/j.matpur.2018.03.005⟩. ⟨hal-01435744⟩
396 Consultations
148 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More