We study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. In this case, the Hamiltonian of the system is neither strictly convex nor coercive. We prove the existence of a weak solution of the MFG system via a vanishing viscosity method and we characterize the distribution of states as the image of the initial distribution by the flow associated with the optimal control.
As a first step we are going to consider the case where the dynamics move in the whole space; after, we will tackle the case where the dynamics are constrained in a given domain.
This is a joint work with: Y. Achdou, P. Mannucci and N. Tchou.