论文标题
千古choquard平均场比赛的质量集中
Mass concentration for Ergodic Choquard Mean-Field Games
论文作者
论文摘要
我们研究了整个空间中定义的二阶平均平均田间游戏系统消失的粘度限制的浓度现象，$ \ mathbb {r}^n $，riesz-type汇总了非局部耦合和外部限制潜力。在这种情况下，游戏的每个玩家都被吸引到拥挤区域，外部潜在的代理商远离原始代理。专注于质量临界状态$ n-γ'<α<n $，我们研究了在消失的粘度极限下的解决方案的行为，即当扩散忽略时。首先，我们将重新验证的解决方案的渐近行为作为$ \ varepsilon \ to0 $，以riesz-type耦合获得了潜在的自由MFG系统的经典解决方案。其次，我们证明质量浓度是在电势的最小值周围。
We study concentration phenomena in the vanishing viscosity limit for second-order stationary Mean-Field Games systems defined in the whole space $\mathbb{R}^N$ with Riesz-type aggregating nonlocal coupling and external confining potential. In this setting, every player of the game is attracted toward congested areas and the external potential discourages agents to be far away from the origin. Focusing on the mass-subcritical regime $N-γ'<α<N$, we study the behavior of solutions in the vanishing viscosity limit, namely when the diffusion becomes negligible. First, we investigate the asymptotic behavior of rescaled solutions as $\varepsilon\to0$, obtaining existence of classical solutions to potential free MFG systems with Riesz-type coupling. Secondly, we prove concentration of mass around minima of the potential.
