Transport equations and connections with mean field games

PDE Seminar
Tuesday, April 4, 2023 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 006
Ben Seeger – University of Texas at Austin – seeger@math.utexas.edu
Gong Chen

Transport equations arise in the modelling of several complex systems, including mean field games. Such equations often involve nonlinear dependence of the solution in the drift. These nonlinear transport equations can be understood by developing a theory for transport equations with irregular drifts. In this talk, I will outline the well-posedness theory for certain transport equations in which the drift has a one-sided bound on the divergence, yielding contractive or expansive behavior, depending on the direction in which the equation is posed. The analysis requires studying the relationship between the transport and continuity equations and the associated ODE flow. The theory is then used to discuss certain nonlinear transport equations arising in the study of finite state-space mean field games. This is joint work with P.-L. Lions.