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

被引：0
|
作者：
Marco Cirant
Roberto Gianni
Paola Mannucci
机构：
[1] Università di Padova,Dipartimento di Matematica “Tullio Levi
[2] Università di Firenze,Civita”
来源：
Dynamic Games and Applications | 2020年 / 10卷
关键词：
Parabolic equations; Backward–forward system; Mean-field games; Hamilton–Jacobi; Fokker–Planck; Congestion problems; 35K40; 35K61; 49N90;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：100 / 119
页数：19
相关论文
共 49 条
  • [21] MIXED NASH GAMES AND SOCIAL OPTIMA FOR LINEAR-QUADRATIC FORWARD-BACKWARD MEAN-FIELD SYSTEMS
    Feng, Xinwei
    Lin, Yiwei
    MATHEMATICAL CONTROL AND RELATED FIELDS, 2024, 14 (03) : 1193 - 1220
  • [22] Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games
    Qingfeng Zhu
    Lijiao Su
    Fuguo Liu
    Yufeng Shi
    Yong’ao Shen
    Shuyang Wang
    Frontiers of Mathematics in China, 2020, 15 : 1307 - 1326
  • [23] Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games
    Zhu, Qingfeng
    Su, Lijiao
    Liu, Fuguo
    Shi, Yufeng
    Shen, Yong'ao
    Wang, Shuyang
    FRONTIERS OF MATHEMATICS IN CHINA, 2020, 15 (06) : 1307 - 1326
  • [24] Mean-Field Dynamo Model in Anisotropic Uniform Turbulent Flow with Short-Time Correlations
    Yushkov, E., V
    Allahverdiyev, R.
    Sokoloff, D. D.
    GALAXIES, 2020, 8 (03):
  • [25] The Connection between Mean-Field Linear-Quadratic-Gaussian Games of Forward and Backward Stochastic Differential Systems
    Du, Kai
    Wu, Zhen
    2017 CHINESE AUTOMATION CONGRESS (CAC), 2017, : 5042 - 5047
  • [26] Viscosity Solutions of a Degenerate Parabolic-Elliptic System Arising in the Mean-Field Theory of Superconductivity
    Charles M. Elliott
    Reiner Schätzle
    Barbara E. E. Stoth
    Archive for Rational Mechanics and Analysis, 1998, 145 : 99 - 127
  • [27] Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity
    Elliott, CM
    Schätzle, E
    Stoth, BEE
    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1998, 145 (02) : 99 - 127
  • [28] Viscosity solutions of a degenerate parabolic-elliptic system arising in the mean-field theory of superconductivity
    Elliott, C.M.
    Schatzle, R.
    Stoth, B.E.E.
    Archive for Rational Mechanics and Analysis, 145 (02):
  • [29] Splitting methods and short time existence for the master equations in mean field games
    Cardaliaguet, Pierre
    Cirant, Marco
    Porretta, Alessio
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (05) : 1823 - 1918
  • [30] A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise
    Pengyan Huang
    Guangchen Wang
    Shujun Wang
    Hua Xiao
    IEEE/CAA Journal of Automatica Sinica, 2024, 11 (03) : 746 - 759
12345