LIPSCHITZ STABILITY FOR DETERMINATION OF STATES AND INVERSE SOURCE PROBLEM FOR THE MEAN FIELD GAME EQUATIONS
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 824-859 |
| Journal / Publication | Inverse Problems and Imaging |
| Volume | 18 |
| Issue number | 4 |
| Online published | Jan 2024 |
| Publication status | Published - Aug 2024 |
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Abstract
In a bounded domain Ω ⊂ ℝd, d ≥ 1, over a time interval (0, T), we consider mean field game equations whose principal coefficients depend on the time and the state variables with a general Hamiltonian. We attach a 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 the associated Dirichlet data on an 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. © 2024, American Institute of Mathematical Sciences. All rights reserved.
Research Area(s)
- Carleman estimate, inverse problems, Mean field games, stability, uniqueness
Citation Format(s)
LIPSCHITZ STABILITY FOR DETERMINATION OF STATES AND INVERSE SOURCE PROBLEM FOR THE MEAN FIELD GAME EQUATIONS. / Imanuvilov, Oleg; Liu, Hongyu; Yamamoto, Masahiro.
In: Inverse Problems and Imaging, Vol. 18, No. 4, 08.2024, p. 824-859.
In: Inverse Problems and Imaging, Vol. 18, No. 4, 08.2024, p. 824-859.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
