Abstract
This is a survey about the theory of density-constrained evolutions in theWasserstein 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.
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