Strong solutions for time-dependent mean field games with non-separable Hamiltonians
Strong solutions for time-dependent mean field games with non-separable Hamiltonians
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具有不可分离哈密顿量的瞬态平均场博弈的强解
DOI：
10.1016/j.matpur.2018.03.003
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
D. Ambrose
中科院分区：
文献类型：
--
作者：
D. Ambrose
证明了具有不可分Hamilton算子的含时平均场对策的强解的存在性定理。在最近的一次声明中，我们证明了具有局部耦合的平均场博弈存在小而强的解。我们首先推广了先前的工作，允许不可分的哈密顿。这个证明的灵感来自于Duchon和Robert关于不可压缩流体力学中小数据涡面存在性的工作。我们的下一个存在性结果是在系统弱耦合的情况下;也就是说，我们允许数据具有任意大小，但要求（仍然可能是不可分的）哈密顿量在某种意义上是小的。这个定理的证明依赖于隐函数定理。
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.