Existence for stationary mean-field games with congestion and quadratic Hamiltonians

被引：34

作者：

Gomes, Diogo A. ^{[1
,2
]}

Mitake, Hiroyoshi ^{[3
]}

机构：

[1] King Abdullah Univ Sci & Technol, CSMSE Div, Thuwal 239556900, Saudi Arabia

[2] KAUST SRI Uncertainty Quantificat Ctr Computat Sc, Thuwal, Saudi Arabia

[3] Hiroshima Univ, Inst Sustainable Sci & Dev, Higashihiroshima 7398527, Japan

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2015年 / 22卷 / 06期

关键词：

Mean-field games; Quadratic Hamiltonians; Congestion;

D O I：

10.1007/s00030-015-0349-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.

引用

页码：1897 / 1910

页数：14

共 22 条

[1] Finite Difference Methods for Mean Field Games [J].

Achdou, Yves .

HAMILTON-JACOBI EQUATIONS: APPROXIMATIONS, NUMERICAL ANALYSIS AND APPLICATIONS, CETRARO, ITALY 2011, 2013, 2074 :1-47

[2] SOME EXISTENCE THEOREMS FOR SEMI-LINEAR ELLIPTIC EQUATIONS [J].

AMANN, H ;

CRANDALL, MG .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1978, 27 (05) :779-790

[3]

[Anonymous], 2011, PREPRINTS

[4] LONG TIME AVERAGE OF MEAN FIELD GAMES [J].

Cardaliaguet, Pierre ;

Lasry, Jean-Michel ;

Lions, Pierre-Louis ;

Porretta, Alessio .

NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (02) :279-301

[5]

Dieudonne J., 1969, Pure and Applied Mathematics, V10-I, pxviii+387

[6]

Gomes D. A., 2013, ARXIV13116684

[7]

Gomes D. A., 2014, COMMUN PART IN PRESS

[8]

Gomes D, 2014, T AM MATH SOC, V366, P903

[9] MATHER MEASURES SELECTED BY AN APPROXIMATION SCHEME [J].

Gomes, Diogo ;

Iturriaga, Renato ;

Sanchez-Morgado, Hector ;

Yu, Yifeng .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (10) :3591-3601

[10] Mean Field Games Models-A Brief Survey [J].

Gomes, Diogo A. ;

Saude, Joao .

DYNAMIC GAMES AND APPLICATIONS, 2014, 4 (02) :110-154

← 1 2 3 →