周期环境下后向平均场博弈系统的均匀化

IF 0.6 4区 数学 Q3 MATHEMATICS
P. Lions, P. Souganidis
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引用次数: 2

摘要

我们研究了(粘性)前后平均场对策系统在小粘性极限和周期环境下的均匀化性质。我们考虑分离的哈密顿量,并为具有(i)“平滑”耦合和一般初始和终端数据的系统,以及(ii)具有“局部耦合”但准备充分的数据的系统提供结果。极限是一阶前向后向系统。在非局部耦合情况下,平均系统是mfg型的,在某些情况下是适定的。对于具有局部耦合的问题,假设正式获得的极限系统具有光滑的解,并且具有准备好的初始和终端数据,则证明了均匀化结果。使用一个非常一般的例子(潜在mfg),还表明极限系统不一定是mfg类型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Homogenization of the backward-forward meanfield games systems in periodic environments
We study the homogenization properties in the small viscosity limit and in periodic environments of the (viscous) backward-forward mean-field games system. We consider separated Hamiltonians and provide results for systems with (i) "smoothing" coupling and general initial and terminal data, and (ii) with "local coupling" but well-prepared data.The limit is a first-order forward-backward system. In the nonlocal coupling case, the averaged system is of mfg-type, which is well-posed in some cases. For the problems with local coupling, the homogenization result is proved assuming that the formally obtained limit system has smooth solutions with well prepared initial and terminal data. It is also shown, using a very general example (potential mfg), that the limit system is not necessarily of mfg-type.
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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