Michael V. Klibanov – författare
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3 produkter
3 produkter
1 844 kr
Kommande
Inverse Problems and Carleman Estimates
Global Uniqueness, Global Convergence and Experimental Data
Inbunden, Engelska, 2021
2 556 kr
Skickas inom 5-8 vardagar
This book summarizes the main analytical and numerical results of Carleman estimates. In the analytical part, Carleman estimates for three main types of Partial Differential Equations (PDEs) are derived. In the numerical part, first numerical methods are proposed to solve ill-posed Cauchy problems for both linear and quasilinear PDEs. Next, various versions of the convexification method are developed for a number of Coefficient Inverse Problems.
Carleman Estimates in Mean Field Games
Stability and Uniqueness for Nonlinear PDEs and Inverse Problems
Inbunden, Engelska, 2025
1 782 kr
Skickas inom 5-8 vardagar
This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields. This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.