In 2010, Aude Roudneff, Bertrand Maury and Filippo Santambrogio proposed a macroscopical model for crowd motion, yielding a new PDE system, rather unclassified at the time. Thanks to their collaboration, they managed to fit this PDE into the Wasserstein gradient flow framework with a JKO scheme. However, there are substantial issues with the model, as people can travel faster than they would spontaneously, contradicting several empiric laws in crowd motion. Realizing the difficulty of remaining in this framework to correct these issues, we tried a whole new approach using conservation law theory. We consider a PDE very similar to LWR models for traffic, with a parameter modeling some kind of anticipation that we take to the stiff limit. We will explain how we managed, in collaboration with Filippo Santambrogio and Benoit Perthame, to obtain estimates that allowed us to pass to the limit and prove existence of solutions for a whole new PDE. We will also try to take the remaining time to discuss how the question about uniqueness remains open, as it seems that we step out of known PDE theory…
