CONVEXIFICATION NUMERICAL METHOD FOR A COEFFICIENT INVERSE PROBLEM FOR THE SYSTEM OF NONLINEAR PARABOLIC EQUATIONS GOVERNING MEAN FIELD GAMES

被引：1

作者：

Klibanov, Michael V. ^{[1
]}

Li, Jingzhi ^{[2
,3
,4
]}

Yang, Zhipeng ^{[5
]}

机构：

[1] Univ North Carolina, Dept Math & Stat, Charlotte, NC 28223 USA

[2] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

[3] Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Peoples R China

[4] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China

[5] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

INVERSE PROBLEMS AND IMAGING | 2025年 / 19卷 / 02期

基金：

中国博士后科学基金;

关键词：

Global convergence; numerical studies; mean field games; RECONSTRUCTION; ALGORITHM;

D O I：

10.3934/ipi.2024031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Mean Field Games theory has applications in mathematical modeling of various social phenomena. The key to this theory is the Mean Field Games System (MFGS) of two coupled nonlinear parabolic Partial Differential Equations with two opposite directions of time. One of those equations contains an integral operator, the so-called global interaction term. The topic of Coefficient Inverse Problems (CIPs) for the MFGS is in its infant age. In this paper, a CIP for the MFGS is solved numerically by a globally convergent convexification method. A coefficient characterizing the global interaction term is recovered from the single measurement data. A detailed global convergence analysis, based on Carleman estimates, is presented. Numerical results demonstrate accurate reconstructions from noisy data.

引用

页码：219 / 252

页数：34

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