LIPSCHITZ STABILITY ESTIMATE AND UNIQUENESS IN THE RETROSPECTIVE ANALYSIS FOR THE MEAN FIELD GAMES

被引：13

作者：

Klibanov, Michael V. ^{[1
]}

Averboukh, Yurii ^{[2
]}

机构：

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

[2] Krasovskii Inst Math & Mech, S Kovalevskaja st,16, Ekaterinburg 620990, Russia

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 01期

关键词：

mean field games system; retrospective analysis; two Carleman estimates; Lipschitz stability estimate; uniqueness; INVERSE PROBLEMS; CARLEMAN;

D O I：

10.1137/23M1554801

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carleman estimates are derived. They allow us to obtain the Lipschitz stability estimate with respect to a possible error in the input initial and terminal data of a retrospective problem for MFGS. This stability estimate, in turn, implies a uniqueness theorem for the problem under consideration. The idea of using Carleman estimates to obtain stability and uniqueness results came from the field of ill-posed and inverse problems.

引用

页码：616 / 636

页数：21

共 40 条

[21]

Klibanov MV, 2024, Arxiv, DOI arXiv:2305.01065

[22]

Klibanov MV, 2023, Arxiv, DOI arXiv:2302.10709

[23] NUMERICAL METHOD FOR A 1D COEFFICIENT [J].

Klibanov, Michael, V ;

Le, Thuy T. ;

Nguyen, Loc H. ;

Sullivan, Anders ;

Nguyen, Lam .

INVERSE PROBLEMS AND IMAGING, 2021,

[24] Carleman estimates for the regularization of ill-posed Cauchy problems [J].

Klibanov, Michael V. .

APPLIED NUMERICAL MATHEMATICS, 2015, 94 :46-74

[25] Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems [J].

Klibanov, Michael V. .

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2013, 21 (04) :477-560

[26]

KLIBANOV MV, 1984, DIFF EQUAT+, V20, P755

[27] INVERSE PROBLEMS AND CARLEMAN ESTIMATES [J].

KLIBANOV, MV .

INVERSE PROBLEMS, 1992, 8 (04) :575-596

[28]

KOLOKOLTSOV V., 2013, Open J. Optim., V2, P39

[29]

Ladyzhenskaya O. A., 1985, Appl. Math. Sci., V49

[30] Mean field games. I - The stationary case. [J].

Lasry, Jean-Michel ;

Lions, Pierre-Louis .

COMPTES RENDUS MATHEMATIQUE, 2006, 343 (09) :619-625

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