Existence of solutions to contact mean-field games of first order

Abstract

This paper deals with the existence of solutions of a class of contact mean-field game systems of first order consisting of a contact Hamilton-Jacobi equation and a continuity equation. Evans found a connection between Hamilton-Jacobi equations and continuity equations from the weak KAM point of view, where the coupling term is zero. Inspired by his work, we prove the main existence result by analyzing the properties of the Mather set for contact Hamiltonian systems.

Keywords

• mean-field games
• weak kam theory
• contact hamiltonian systems
• existence
• 37j51
• 35q89