Short-Time Existence for a General Backward-Forward Parabolic System Arising from Mean-Field Games

被引：12

作者：

Cirant, Marco ^{[1
]}

Gianni, Roberto ^{[2
]}

Mannucci, Paola ^{[1
]}

机构：

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

[2] Univ Firenze, Dipartimento Matemat & Informat U Dini, Florence, Italy

来源：

DYNAMIC GAMES AND APPLICATIONS | 2020年 / 10卷 / 01期

关键词：

Parabolic equations; Backward-forward system; Mean-field games; Hamilton-Jacobi; Fokker-Planck; Congestion problems;

D O I：

10.1007/s13235-019-00311-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the local in time existence of a regular solution of a nonlinear parabolic backward-forward system arising from the theory of mean-field games (briefly MFG). The proof is based on a contraction argument in a suitable space that takes account of the peculiar structure of the system, which involves also a coupling at the final horizon. We apply the result to obtain existence to very general MFG models, including also congestion problems.

引用

页码：100 / 119

页数：20

共 49 条

[1] Short-Time Existence for a General Backward–Forward Parabolic System Arising from Mean-Field Games
Marco Cirant
Roberto Gianni
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Dynamic Games and Applications, 2020, 10 : 100 - 119
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