# American Institute of Mathematical Sciences

June  2012, 7(2): 263-277. doi: 10.3934/nhm.2012.7.263

## A semi-discrete approximation for a first order mean field game problem

 1 "Sapienza", Università di Roma, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, 00161 Roma 2 "Sapienza", Università di Roma, Dipartimento di Matematica Guido Castelnuovo, 00185 Rome, Italy

Received  November 2011 Revised  March 2012 Published  June 2012

In this article we consider a model first order mean field game problem, introduced by J.M. Lasry and P.L. Lions in [18]. Its solution $(v,m)$ can be obtained as the limit of the solutions of the second order mean field game problems, when the noise parameter tends to zero (see [18]). We propose a semi-discrete in time approximation of the system and, under natural assumptions, we prove that it is well posed and that it converges to $(v,m)$ when the discretization parameter tends to zero.
Citation: Fabio Camilli, Francisco Silva. A semi-discrete approximation for a first order mean field game problem. Networks & Heterogeneous Media, 2012, 7 (2) : 263-277. doi: 10.3934/nhm.2012.7.263
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