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

2023/04/13 by Imanuvilov, Oleg, Liu, Hongyu, Yamamoto, Masahiro
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.06673

Abstract

We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in Ω× (0,T) whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where Ω is a bounded domain in \Bbb R^d and (0,T) is the time interval. 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 intermediate time.

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