Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters

Abstract : A few applications of the viability theory to the solution to the Hamilton-Jacobi-Moskowitz problems are presented. In the considered problem the Hamiltonian (fundamental diagram) depends on time, position and/or some regulation parameters. We study such a problem in its equivalent variational formulation. In this case, the corresponding lagrangian depends on the state of the characteristic dynamical system. As the Lax-Hopf formulae that give the solution in a semi-explicit form for an homogeneous lagrangian do not hold, a capture basin algorithm is proposed to compute the Moskowitz function as a viability solution of the Hamilton-Jacobi-Moskowitz problem with general conditions (including initial, boundary and internal conditions). We present two examples of applications to traffic regulation problems.
Type de document :
Article dans une revue
Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2013, 8 (3), pp.707-726. 〈10.3934/nhm.2013.8.707〉
Liste complète des métadonnées

https://hal-ensta.archives-ouvertes.fr/hal-00966735
Contributeur : Aurélien Arnoux <>
Soumis le : jeudi 27 mars 2014 - 11:16:38
Dernière modification le : mercredi 6 décembre 2017 - 16:46:01

Lien texte intégral

Identifiants

Collections

Citation

Anna Désilles. Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2013, 8 (3), pp.707-726. 〈10.3934/nhm.2013.8.707〉. 〈hal-00966735〉

Partager

Métriques

Consultations de la notice

110