Lipschitz Stability Estimate and Uniqueness in the Retrospective Analysis for the Mean Field Games System via Two Carleman Estimates
Michael V. Klibanov, Yurii Averboukh
Abstract
.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.Keywordsmean field games systemretrospective analysistwo Carleman estimatesLipschitz stability estimateuniquenessMSC codes91A1635R30