Second order mean field games with degenerate diffusion and local coupling

Cardaliaguet, Pierre; Graber, Philip Jameson; Porretta, Alessio; Tonon, Daniela

Cardaliaguet, Pierre; Graber, Philip Jameson; Porretta, Alessio; Tonon, Daniela (2015), Second order mean field games with degenerate diffusion and local coupling, Nonlinear Differential Equations and Applications NoDEA, 22, 5, p. 1287-1317. 10.1007/s00030-015-0323-4

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1407.7024v1

Date

2015

Journal name

Nonlinear Differential Equations and Applications NoDEA

Volume

Number

Publisher

Springer

Pages

1287-1317

Publication identifier

10.1007/s00030-015-0323-4

Metadata

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Author(s)

Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Graber, Philip Jameson
Unité de Mathématiques Appliquées [UMA]
Porretta, Alessio
Dipartimento di Matematica [Roma II] [DIPMAT]
Tonon, Daniela
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Abstract (EN)

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.

Subjects / Keywords

MFG weak solutions