Maria Pia Gualdani
(Austin, USA)

Global Existence of a Free Boundary Problem with Non-Standard Sources

We consider a nonlinear free boundary problem, proposed by J.M.Lasry and P.L. Lions in 2006 in the framework of mean field games. The model describes the evolution of a scalar price which is realized as a free boundary of a diffusion equation with evolving sources. The talk focuses on global existence, uniqueness and regularity of solutions. The proof uses tools from non-interacting stochastic particle systems and multiscale analysis. Joint work with L. Chayes, M.d.M. Gonzalez and I. Kim.