Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902404 | Journal de Mathématiques Pures et Appliquées | 2018 | 14 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
David M. Ambrose,