期刊
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
卷 21, 期 3, 页码 690-722出版社
EDP SCIENCES S A
DOI: 10.1051/cocv/2014044
关键词
Mean field games; Hamilton-Jacobi equations; optimal control; nonlinear PDE; transport theory; long time average
资金
- Commission of the European Communities under the 7th Framework Programme Marie Curie Initial Training Networks Project SADCO, FP7-PEOPLE-2010-ITN [264735]
- French National Research Agency [ANR-10-BLAN 0112, ANR-12-BS01-0008-01]
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.
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