论文标题
KAM弱方法对具有状态限制的一阶平均现场游戏
Weak KAM approach to first-order Mean Field Games with state constraints
论文作者
论文摘要
随着时间范围$ t $的无限，我们研究了限制的MFG系统解决方案的渐近行为。为此，我们从弱KAM理论的角度分析了具有状态限制的汉密尔顿 - 雅各比方程，从而为相关的变异问题构建了马瑟量度。使用这些结果，我们表明存在解决受约束的Ergodic平均野外游戏系统的解决方案，而沿阵行常数是唯一的。最后，我们证明，$ [0，t] $上一阶约束MFG问题的任何解决方案将$ t \ to +\ \ iftty $的解决方案收敛到ergodic系统的解决方案。
We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on $[0,T]$ converges to the solution of the ergodic system as $T \to +\infty$.
