Diogo Gomes, Professor, Applied Mathematics and Computational Science King Abdullah University of Science and Technology

Chensong Zhang, Professor

Weak-strong uniqueness for mean-field games

10:00-11:00 June 24 (Monday), S813

We address the uniqueness of stationary first-order Mean-Field Games (MFGs). Despite well-established existence results, establishing uniqueness, particularly for weaker solutions in the sense of monotone operators, remains an open challenge. Building upon the framework of monotonicity methods, we introduce a linearization method that enables us to prove a weak-strong uniqueness result for stationary MFG systems. In particular, we give explicit conditions under which this uniqueness holds.

Bio：Professor Diogo Gomes is a Professor of Applied Mathematics and Computational Science at KAUST. He obtained his Ph.D. in Mathematics from the University of California at Berkeley, completed postdoctoral research at the Institute for Advanced Study in Princeton and the University of Texas at Austin. Professor Gomes’s research interests are in partial differential equations (PDE), namely on viscosity solutions of elliptic, parabolic and Hamilton-Jacobi equations as well as in related mean-field models. This area includes a large class of PDEs and examples, ranging from classical linear equations to highly nonlinear PDEs, including the Monge-Ampere equation, geometric equations for image processing, non-linear elasticity equations and the porous media equation.