Weak KAM theory for potential MFG

被引：8

作者：

Cardaliaguet, Pierre ^{[1
]}

Masoero, Marco ^{[1
]}

机构：

[1] Univ Paris 09, CEREMADE, PSL Res Univ, Pl Lattre de Tassigny, F-75016 Paris, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 07期

关键词：

MEAN-FIELD GAMES; LONG-TIME AVERAGE; CONVERGENCE; TORUS;

D O I：

10.1016/j.jde.2019.09.060

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：3255 / 3298

页数：44

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