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Carleman Estimates in Mean Field Games : Stability and Uniqueness for Nonlinear PDEs and Inverse Problems.
- Format:
- Book
- Author/Creator:
- Klibanov, M. V. (Michael V.)
- Series:
- Inverse and Ill-Posed Problems Series
- Inverse and Ill-Posed Problems Series ; v.64
- Language:
- English
- Subjects (All):
- Mean field theory.
- Inverse problems (Differential equations).
- Physical Description:
- 1 online resource (160 pages)
- Edition:
- 1st ed.
- Place of Publication:
- Berlin/Boston : Walter de Gruyter GmbH, 2025.
- Summary:
- This book explores the advanced mathematical framework of Carleman estimates in the context of Mean Field Games (MFG) theory. Authored by Michael V. Klibanov and Jingzhi Li, it presents analytical and numerical studies related to forward problems and coefficient inverse problems within MFG systems. The authors address solutions to coupled nonlinear parabolic Partial Differential Equations (PDEs), tackling challenges such as stability, uniqueness, and existence. The book integrates ill-posed problem theory and introduces calibration methods using single measurement data. Applications of MFG theory span diverse fields including finance, sociology, election dynamics, electric vehicle interactions, combating corruption, and deep learning. Targeted toward mathematicians and researchers in applied mathematics, this work advances the understanding of societal phenomena through mathematical modeling. Generated by AI.
- Contents:
- Preface
- Acknowledgment
- Contents
- 1 Retrospective problem of mean field games
- 2 Stability and uniqueness for semiforecasting and forecasting problems
- 3 Hölder stability and uniqueness for the case of lateral Cauchy data
- 4 Hölder stability for a coefficient inverse problem for the mean field games system
- 5 Convexification numerical method for the retrospective problem for mean field games
- 6 Convexification for a coefficient inverse problem for mean field games
- Bibliography
- Index Generated by AI.
- Notes:
- Part of the metadata in this record was created by AI, based on the text of the resource.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-11-172311-9
- OCLC:
- 1521233857
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