Séminaire Jeunes chercheurs (Guillaume Soenen, jeudi 10 avril 2025)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 10 avril 2025 à 17h en salle A707. Nous aurons le plaisir d'écouter Guillaume Soenen (CEREMADE), qui nous parlera de

Hydrodynamic limit of a particle system

Abstract
In this talk, we consider a particle system where particles evolve along a line at constant speed. This system has already been studied with some boundary conditions (particles on a torus or confined between two walls), but we propose here an unsolved problem, where the particles are evolving between a wall on one side and some pressure force on the other side. As this system is not easy to understand, we add a thermalization phenomenon, ie some probabilistic term in the equation (here it will be Langevin dynamics). The goal is to compute the hydrodynamic limit of this system : the idea is to describe the macroscopic behavior from the microscopic equations. It will lead us to study a free boundary partial differential equation and the uniqueness of its weak solutions.