Inserted: 7 jan 2018
Last Updated: 7 jan 2018
This survey corresponds to some talks I recently gave in different seminars and workshops, and in particular at the SMAI 2017 French meeting : this survey has been written for and submitted to the proceedings of such conference.
This is a survey about the theory of density-constrained evolutions in the Wasserstein space developed by B. Maury, the author, and their collaborators as a model for crowd motion. Connections with microscopic models and other PDEs are presented, as well as several time-discretization schemes based on variational techniques, together with the main theorems guaranteeing their convergence as a tool to prove existence results. Then, a section is devoted to the uniqueness question, and a last one to different numerical methods inspired by optimal transport.
Keywords: Optimal transport, Gradient flows, hele-shaw, Entropic regularization, pedestrian movement, sweeping process, splitting schemes, augmented lagrangian, semidiscrete transport