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Mean field games systems of first order

Cardaliaguet, Pierre; Graber, Philip Jameson (2015), Mean field games systems of first order, ESAIM. COCV, 21, 3, p. 690-722. 10.1051/cocv/2014044

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
https://arxiv.org/abs/1401.1789v1
Date
2015
Nom de la revue
ESAIM. COCV
Volume
21
Numéro
3
Éditeur
EDP sciences
Ville d’édition
Paris
Pages
690-722
Identifiant publication
Métadonnées
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Auteur(s)
Cardaliaguet, Pierre
Graber, Philip Jameson
Résumé (EN)
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.
Mots-clés
nonlinear PDE; optimal control; transport theory; long time average; Hamilton-Jacobi equations; mean field games