具有不可分局部哈密顿量的运动型平均场对策

IF 1.2 2区 数学 Q1 MATHEMATICS
David M. Ambrose, Megan Griffin-Pickering, Alpár R. Mészáros
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引用次数: 0

摘要

我们63证明了一类动力学型平均场博弈(mfg)的适定性,这类博弈通常出现在智能体控制其加速度时。这样的系统包括表示空间位置和速度的独立变量。我们考虑没有任何结构条件的不可分离哈密顿量,它局部依赖于密度变量。我们的分析基于两个主要成分:一方面是Sobolev空间中前向-后向系统的能量方法,另一方面是控制相对于速度变量的导数的合适向量场方法。这两种技术的仔细结合揭示了适用于涉及一般漂移-扩散算子和非线性的mfg的有趣现象。虽然许多一般mfg系统的先验存在理论认为最终基准函数是平滑的,但我们可以允许该函数是非平滑的,即也局部依赖于最终测量。我们的适定性结果在一个适当的小条件下成立,在数据上共同假设。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Kinetic-type mean field games with non-separable local Hamiltonians

Kinetic-type mean field games with non-separable local Hamiltonians

Kinetic-type mean field games with non-separable local Hamiltonians

Kinetic-type mean field games with non-separable local Hamiltonians

We prove well-posedness of a class of kinetic-type mean field games (MFGs), which typically arise when agents control their acceleration. Such systems include independent variables representing the spatial position as well as velocity. We consider non-separable Hamiltonians without any structural conditions, which depend locally on the density variable. Our analysis is based on two main ingredients: an energy method for the forward–backward system in Sobolev spaces, on the one hand, and on a suitable vector field method to control derivatives with respect to the velocity variable, on the other hand. The careful combination of these two techniques reveals interesting phenomena applicable for MFGs involving general classes of drift-diffusion operators and non-linearities. While many prior existence theories for general MFGs systems take the final datum function to be smoothing, we can allow this function to be non-smoothing, that is, also depending locally on the final measure. Our well-posedness results hold under an appropriate smallness condition, assumed jointly on the data.

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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
186
审稿时长
6-12 weeks
期刊介绍: The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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