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- Title
Stability in determination of states for the mean field game equations.
- Authors
Liu, Hongyu; Yamamoto, Masahiro
- Abstract
We consider solutions satisfying the Neumann zero boundary condition and a linearized mean field game system in $ \Omega \times (0, T) $, where $ \Omega $ is a bounded domain in $ \mathbb{R}^d $ and $ (0, T) $ is the time interval. We prove two kinds of stability results in determining the solutions. The first is Hölder stability in time interval $ (\varepsilon, T) $ with arbitrarily fixed $ \varepsilon>0 $ by data of solutions in $ \Omega \times \{T\} $. The second is the Lipschitz stability in $ \Omega \times (\varepsilon, T- \varepsilon) $ by data of solutions in arbitrarily given subdomain of $ \Omega $ over $ (0, T) $.
- Subjects
MEAN field theory; NEUMANN boundary conditions; EQUATIONS; STABILITY of linear systems; MATHEMATICAL constants
- Publication
Communications on Analysis & Computation (CAC), 2023, Vol 1, Issue 2, p1
- ISSN
2837-0562
- Publication type
Article
- DOI
10.3934/cac.2023009