Variational problems and PDEs arising in congested transport models

Series: 
PDE Seminar
Thursday, April 12, 2012 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Universite de Paris IX (Paris-Dauphine)
Organizer: 
In this talk, I will describe several models arising in congested transport problems. I will first describe static models which lead to some highly degenerate elliptic PDEs. In the second part of the talk, I will address dynamic models which can be seen as a generalization of the Benamou-Brenier formulation of the quadratic optimal transport problem and will discuss the existence and regularity of the adjoint state. The talk will be based on several joint works with Lorenzo Brasco, Pierre Cardaliaguet, Bruno Nazaret and Filippo Santambrogio.