Non-coercive first order Mean Field Games

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Mannucci, Paola¹  Marchi, Claudio²  Mariconda, Carlo¹  Tchou, Nicoletta³ 

[1] Univ Padua, Dipartimento Matemat Tullio Levi Civita, I-35121 Padua, Italy

[2] Univ Padua, Dipartimento Ingn Informaz, I-35131 Padua, Italy

[3] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France

关键词: Mean Field Games;    First order Hamilton-Jacobi equations;    Continuity equation;    Non-coercive Hamiltonian;    Degenerate optimal control problem;   

DOI  :  10.1016/j.jde.2020.03.035

来源: Elsevier

【 摘 要 】

We study first order evolutive Mean Field Games where the Hamiltonian are non-coercive. This situation occurs, for instance, when some directions are forbidden to the generic player at some points. We establish the existence of a weak solution of the system via a vanishing viscosity method and, mainly, we prove that the evolution of the population's density is the push-forward of the initial density through the flow characterized almost everywhere by the optimal trajectories of the control problem underlying the Hamilton-Jacobi equation. As preliminary steps, we need to prove that the optimal trajectories for the control problem are unique (at least for a.e. starting points) and that the corresponding unique optimal control has a feedback expression in terms of the intrinsic gradient of the value function. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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