Georgia Institute of Technology College of Sciences

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.