Lipschitz stability for determination of states and inverse source problem for the mean field game equations

2023/07/10 by Imanuvilov, Oleg, Liu, Hongyu, Yamamoto, Masahiro · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.04641

Abstract

In a bounded domain Ω⊂ ℝ^d over time interval (0,T), we consider mean field game equations whose principal coefficients depend on the time and state variables with a general Hamiltonian. We attach the non-zero Robin boundary condition. We first prove the Lipschitz stability in Ω× (ε, T-ε) with given ε>0 for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of ∂Ω. Next we prove the Lipschitz stability for an inverse problem of determining spatially varying factors of source terms and a coefficient by extra boundary data and spatial data at an intermediate time.

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• Truncated Differentiation for Inverse Potential MFGs
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