Stability in determination of states for the mean field game equations

2023/04/12 by Hongyu Liu, Masahiro Yamamoto, Liu, Hongyu +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2304.05896

openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider solutions satisfying the Neumann zero boundary condition and a linearized mean field game system in Ω× (0,T), where Ω is a bounded domain in 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 (ε, T) with arbitrarily fixed ε>0 by data of solutions in Ω× \T\. The second is the Lipschitz stability in Ω× (ε, T-ε) by data of solutions in arbitrarily given subdomain of Ω over (0,T).

Related

• Lipschitz stability for determination of states and inverse source problem for the mean field game equations
• Lipschitz stability for determination of states and inverse source problem for the mean field game equations
• Mean field games under invariance conditions for the state space
• The Mean Field Games System: Carleman Estimates, Lipschitz Stability and Uniqueness
• Global Lipschitz stability for an inverse coefficient problem for a mean field game system