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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2015

Second order mean field games with degenerate diffusion and local coupling

Résumé

We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as minimizers of two optimal control problems. We also show that such solutions are stable with respect to the data, so that in particular the degenerate case can be approximated by a uniformly parabolic (viscous) perturbation.
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Dates et versions

hal-01049834 , version 1 (25-07-2014)

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Pierre Cardaliaguet, J. Graber, Alessio Porretta, Daniela Tonon. Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differential Equations and Applications, 2015, 22 (5), pp.1287-1317. ⟨hal-01049834⟩
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