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arXiv · 2304.06673

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

Oleg Imanuvilov·Hongyu Liu·Masahiro Yamamoto
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Abstract

We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\Omega \times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where $\Omega$ is a bounded domain in $\Bbb R^d$ and $(0,T)$ is the time interval. We first prove the Lipschitz stability in $\Omega \times (\varepsilon, T-\varepsilon)$ with given $\varepsilon>0$ for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of $\partial\Omega$. 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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Oleg Imanuvilov, Hongyu Liu, Masahiro Yamamoto. 2023-04-13. Lipschitz stability for determination of states and inverse source problem for the mean field game equations. https://arxiv.org/abs/2304.06673

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