Calculus of Variations and Geometric Measure Theory
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F. Santambrogio

Crowd motion and evolution PDEs under density constraints

created by santambro on 07 Jan 2018
modified on 04 Apr 2018


Accepted Paper

Inserted: 7 jan 2018
Last Updated: 4 apr 2018

Journal: proceedings of the 2017 SMAI conference
Year: 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 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


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