Strong solutions for time-dependent mean field games with non-separable Hamiltonians

被引:25
作者
Ambrose, David M. [1 ]
机构
[1] Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USA
来源
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 113卷
基金
美国国家科学基金会;
关键词
Mean field games; Perturbations; Implicit function theorem; Strong solutions;
D O I
10.1016/j.matpur.2018.03.003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove existence theorems for strong solutions of time-dependent mean field games with non-separable Hamiltonian. In a recent announcement, we showed existence of small, strong solutions for mean field games with local coupling. We first generalize that prior work to allow for non-separable Hamiltonians. This proof is inspired by the work of Duchon and Robert on the existence of small-data vortex sheets in incompressible fluid mechanics. Our next existence result is in the case of weak coupling of the system; that is, we allow the data to be of arbitrary size, but instead require that the (still possibly non-separable) Hamiltonian be small in a certain sense. The proof of this theorem relies upon an appeal to the implicit function theorem. (C) 2018 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:141 / 154
页数:14
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