2018/05/28 by Yiru Cai, Cai, Yiru, Haobo Qi +5
Mathematics · Physics and Astronomy · #91A13 #91A25 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.DS #math.OC #msc:91A13 #msc:91A25
paper · pdf · doi:10.48550/arxiv.1805.11068
17 pages
arxiv created 2018/05/28 · openalex publication_date 2018/05/28 · arxiv updated 2018/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the one-dimensional stationary first-order mean-field game (MFG) system with the coupling between the Hamilton-Jacobi equation and the transport equation. In both cases that the coupling is strictly increasing and decreasing with respect to the density of the population, we show that when the potential vanishes the regular solution of MFG system converges to the one of the corresponding integrable MFG system. Furthermore, we obtain the convergence rate of such limit.