Société de Mathématiques Appliquées et Industrielles

19ème journée EDP/Probas

Modèles de champ moyen

vendredi 20 mai 2016

10h - 12h Stéphane Mischler (Paris Dauphine) : Quantitative, qualitative and uniform in time propagation of chaos

I will review some old and recent papers on the propagation of chaos issue. I will discuss the different methods and how they may answer the three fundamental problems which are to get quantitative, qualitative and uniform in time propagation of chaos. My talk will be illustrated by application to (possibly singular) McKean-Vlasov and Boltzmann models.

14h15 - 16h15 Giambattista Giacomin (Paris Diderot) : Mean field models of oscillators and excitable units

I will present models, motivated by biophysics and life sciences, of interacting oscillators and of the interacting dynamical systems going under the name of (noisy) excitable units. I will then focus on long time behavior, both when the number N of interacting components is large, but finite, and in the N equal to infinity limit. In both cases the central keyword of the analysis is "synchronization". I will focus both on properties of the PDE arising in the limit, notably on stable periodic behavior, and on the breakdown of the PDE approximation beyond finite time horizon, that is when time becomes large with N.

La journée aura lieu dans l’amphithéâtre Darboux de l’Institut Henri Poincaré, 11 rue Pierre et Marie Curie, Paris 5ème (accès).

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