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Strong solutions for time-dependent mean field games with non-separable Hamiltonians
Journal article   Open access   Peer reviewed

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

David M. Ambrose
Journal de mathématiques pures et appliquées, v 113
01 May 2018
url
https://doi.org/10.1016/j.matpur.2018.03.003View
Published, Version of Record (VoR)Open Access (Publisher-Specific) Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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.

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Mathematics
Mathematics, Applied
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