Mean field games systems of first order

Philip Jameson Graber and Pierre Cardaliaguet
submitted
Publication type:
Paper in peer-reviewed journals
Journal:
ESAIM: Control, Optimisation, and Calculus of Variations
Keywords :
mean field games, Hamilton-Jacobi equations, optimal control, nonlinear PDE, transport theory, long time average
Abstract:
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{Gra-Car-2200,
    author={Philip Jameson Graber and Pierre Cardaliaguet },
    title={Mean field games systems of first order },
    journal={ESAIM: Control, Optimisation, and Calculus of Variations },
    year={submitted },
    month={1},
}