Friday, March 24 at 2:00pm to 3:00pm
Kaprielian Hall (KAP), 414
3620 South Vermont Avenue, Los Angeles, CA 90089
Alpar Richard Meszaros, UCLA
In this talk I will present how the theory of optimal transport can be used to study some PDE systems (not necessarily having a gradient flow structure) describing the evolution of the density of a population subject to a density constraint. In this context a particular emphasis will be on a Fokker-Planck type equation. From the modeling point of view this equation can describe the movement of a crowd in a bounded domain, when individuals try to follow a given spontaneous velocity field, but are subject to a Brownian diffusion and - to avoid congestion - have to adapt to a density constraint. From the mathematical point of view, a pressure gradient appears in the PDE (active only in the saturated zones) which affects the movement. The presented results are based on joint works with F. Santambrogio (Paris-Sud, Orsay) and with S. Di Marino (SNS, Pisa).