Convexification for a coefficient inverse problem for a system of two nonlinear

被引：1
|
作者：
Klibanov, Michael V. [1 ]
Li, Jingzhi [2 ,3 ,4 ]
Yang, Zhipeng [5 ]
机构：
[1] Univ North Carolina Charlotte, 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：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2025年 / 179卷
关键词：
A nonlinear parabolic system; Carleman estimates; Convexification numerical method; Global convergence analysis; Numerical experiments; MEAN-FIELD GAMES; RECONSTRUCTION; STABILITY; ALGORITHM;
D O I：
10.1016/j.camwa.2024.12.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in theory and computations. A numerical method for this CIP is developed. Convergence analysis ensures the global convergence of this method. Numerical experiments are presented.
引用
收藏
页码：41 / 58
页数：18
相关论文
共 50 条
  • [1] CONVEXIFICATION NUMERICAL METHOD FOR A COEFFICIENT INVERSE PROBLEM FOR THE SYSTEM OF NONLINEAR PARABOLIC EQUATIONS GOVERNING MEAN FIELD GAMES
    Klibanov, Michael V.
    Li, Jingzhi
    Yang, Zhipeng
    INVERSE PROBLEMS AND IMAGING, 2025, 19 (02) : 219 - 252
  • [2] Convexification of a 3-D coefficient inverse scattering problem
    Klibanov, Michael, V
    Kolesov, Aleksandr E.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 77 (06) : 1681 - 1702
  • [3] Convexification for the viscocity solution for a coefficient inverse problem for the radiative transfer equation
    Klibanov, Michael, V
    Li, Jingzhi
    Yang, Zhipeng
    INVERSE PROBLEMS, 2023, 39 (12)
  • [4] Convexification Numerical Method for a Coefficient Inverse Problem for the Radiative Transport Equation
    Klibanov, Michael V.
    Li, Jingzhi
    Nguyen, Loc H.
    Yang, Zhipeng
    SIAM JOURNAL ON IMAGING SCIENCES, 2023, 16 (01): : 35 - 63
  • [5] Convexification for an inverse parabolic problem
    Klibanov, Michael, V
    Li, Jingzhi
    Zhang, Wenlong
    INVERSE PROBLEMS, 2020, 36 (08)
  • [6] Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation
    Klibanov, Michael V.
    Li, Jingzhi
    Nguyen, Loc H.
    Romanov, Vladimir
    Yang, Zhipeng
    SIAM JOURNAL ON IMAGING SCIENCES, 2023, 16 (03): : 1762 - 1790
  • [7] CONVEXIFICATION FOR A 1D HYPERBOLIC COEFFICIENT INVERSE PROBLEM WITH SINGLE MEASUREMENT DATA
    Smirnov, Alexey
    Klibanov, Michael
    Loc Nguyen
    INVERSE PROBLEMS AND IMAGING, 2020, 14 (05) : 913 - 938
  • [8] An inverse coefficient problem with nonlinear parabolic equation
    Jing L.
    Youjun X.
    Journal of Applied Mathematics and Computing, 2010, 34 (1-2) : 195 - 206
  • [9] A new version of the convexification method for a 1D coefficient inverse problem with experimental data
    Klibanov, Michael, V
    Kolesov, Aleksandr E.
    Sullivan, Anders
    Nguyen, Lam
    INVERSE PROBLEMS, 2018, 34 (11)
  • [10] An inverse coefficient problem for a nonlinear parabolic variational inequality
    Hasanov, Alemdar
    Liu, Zhenhai
    APPLIED MATHEMATICS LETTERS, 2008, 21 (06) : 563 - 570
12345