Journal article
Strong solutions for time-dependent mean field games with non-separable Hamiltonians
Journal de mathématiques pures et appliquées, v 113
01 May 2018
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. (C) 2018 Elsevier Masson SAS. All rights reserved.
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Details
- Title
- Strong solutions for time-dependent mean field games with non-separable Hamiltonians
- Creators
- David M. Ambrose - Drexel University
- Publication Details
- Journal de mathématiques pures et appliquées, v 113
- Publisher
- Elsevier
- Number of pages
- 14
- Grant note
- DMS-1515849 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000431162500004
- Scopus ID
- 2-s2.0-85044051351
- Other Identifier
- 991019168650204721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied