Mean field games systems of first order
2015
Type de publication :
Article (revues avec comité de lecture)
Journal :
ESAIM: Control, Optimisation and Calculus of Variations, vol. 21 (3), pp. 690–722
Editeur :
EDP Sciences
Lien externe :
HAL :
arXiv :
Mots clés :
long time average; mean field games; Hamilton-Jacobi equations; optimal control; nonlinear PDE; transport theory; long time average.;
Résumé :
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.
BibTeX :
@article{Car-Gra-2015,
author={Pierre Cardaliaguet and Philip Jameson Graber },
title={Mean field games systems of first order },
journal={ESAIM: Control, Optimisation and Calculus of Variations },
year={2015 },
volume={21 (3) },
pages={690–722},
}