A  semi-Lagrangian scheme for a degenerate second order mean field game system

Elisabetta Carlini; Francisco J. Silva

doi:10.3934/dcds.2015.35.4269

Article Contents

2015, Volume 35, Issue 9: 4269-4292. Doi: 10.3934/dcds.2015.35.4269

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A semi-Lagrangian scheme for a degenerate second order mean field game system

Elisabetta Carlini^1, and
Francisco J. Silva^2,

1.
"Sapienza" Università di Roma, Dipartimento di Matematica, P.le A. Moro 5, 00185 Roma
2.
XLIM - DMI UMR CNRS 7252, Faculté des Sciences et Techniques, Université de Limoges, 123 Avenue Albert Thomas, 87060-Limoges Cedes

Received: March 31, 2014

Revised: August 31, 2014

Published: May 2017

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Abstract

In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove a convergence result. Some numerical simulations are provided, evidencing the convergence of the approximation and also the difference between the numerical results for the degenerate and non-degenerate cases.

Keywords:

Mathematics Subject Classification: Primary: 65M12, 91A13; Secondary: 65M25, 91A23, 49J15, 35F21, 35Q84.

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