Volume 21, Number 3, July-September 2015
|Page(s)||690 - 722|
|Published online||20 May 2015|
Mean field games systems of first order
Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny,
Paris cedex 16,
2 Commands team (ENSTA ParisTech, INRIA Saclay), 828, Boulevard des Maréchaux, 91762 Palaiseau cedex, France
Revised: 23 July 2014
We consider a first-order 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.
Mathematics Subject Classification: 35Q91 / 49K20
Key words: Mean field games / Hamilton−Jacobi equations / optimal control / nonlinear PDE / transport theory / long time average
© EDP Sciences, SMAI, 2015
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