In this talk we present well posedness of Measure Differential Equations, i.e. evolution equations in the Wasserstein space of probability measures driven by dissipative probability vector fields. We take inspiration from the theory of \emph{dissipative operators} in Hilbert spaces and of Wasserstein gradient flows of geodesically convex functionals. Our approach is based on a measure-theoretic…

Iterative Bregman projections is a classical method to compute  Bregman projections onto an intersection of affine sets. In statistics it was applied to the adjustment of distributions to a priori known marginals, and is best known as the Iterative proportional fitting procedures. In this talk I will present novel results concerning such classical method as well…

In this joint ongoing work with Nicolas Forcadel (INSA Rouen) we study traffic flows models with a bifurcation. The model consists in a single incoming road divided after a junction into several outgoing ones. There are basically two classes of models to describe this situation: microscopic models, which explain how each vehicle behaves  in function…

In this talk we propose a model for the simulation of retinal prostheses based on the use  of organic polymer nanoparticles (NP). The model consists of a nonlinearly coupled system of elliptic partial differential equations accounting for: (1) light photoconversion into free charged carriers in the NP bulk; (2) charge transport in the NP bulk…