Skip to main content

Research Repository

Advanced Search

Advection-diffusion equations with density constraints

Mészáros, Alpár Richárd; Santambrogio, Filippo


Filippo Santambrogio


In the spirit of the macroscopic crowd motion models with hard congestion (i.e., a strong density constraint ρ≤1) introduced by Maury et al. some years ago, we analyze a variant of the same models where diffusion of the agents is also taken into account. From the modeling point of view, this means that individuals try to follow a given spontaneous velocity, but are subject to a Brownian diffusion, and have to adapt to a density constraint which introduces a pressure term affecting the movement. From the point of view of PDEs, this corresponds to a modified Fokker–Planck equation, with an additional gradient of a pressure (only living in the saturated zone {ρ=1}) in the drift. We prove existence and some estimates, based on optimal transport techniques.


Mészáros, A. R., & Santambrogio, F. (2016). Advection-diffusion equations with density constraints. Analysis & PDE, 9(3), 615-644.

Journal Article Type Article
Acceptance Date Feb 9, 2016
Online Publication Date Jun 17, 2016
Publication Date 2016
Deposit Date Oct 1, 2019
Journal Analysis and PDE
Print ISSN 2157-5045
Electronic ISSN 2157-5045
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 9
Issue 3
Pages 615-644
Related Public URLs