Level-set convex Hamilton-Jacobi equations on networks - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

Level-set convex Hamilton-Jacobi equations on networks

Résumé

The paper deals with Hamilton-Jacobi equations on networks with level-set convex (in the gradient variable) Hamiltonians which can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general \emph{vertex condition} is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free paremeter, the \emph{flux limiter}. Second, a general method for proving comparison principles for \emph{flux-limited vertex conditions} is introduced. This method consists in constructing a \emph{vertex test function} to be used in the doubling variable approach. With such a theory and such a method in hand, a very general existence and uniqueness results is derived for Hamilton-Jacobi equations on networks. It also opens many perspectives for the study of these equations in such a singular geometrical framework. To illustrate this fact, we derive for instance a homogenization result for networks.
Fichier principal
Vignette du fichier
IM-14jan16.pdf (527.75 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00832545 , version 1 (10-06-2013)
hal-00832545 , version 2 (17-01-2014)
hal-00832545 , version 3 (24-06-2014)
hal-00832545 , version 4 (10-10-2014)
hal-00832545 , version 5 (10-02-2016)
hal-00832545 , version 6 (29-07-2017)

Identifiants

Citer

Cyril Imbert, Régis Monneau. Level-set convex Hamilton-Jacobi equations on networks. 2014. ⟨hal-00832545v2⟩
708 Consultations
515 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More