Séminaire EDP du CAMS 2017/2018

Ce séminaire réunit les chercheurs du Centre d’analyse et de mathématique sociales (CAMS) et est destiné à un public de spécialistes des équations aux dérivées partielles non linéaires. Les exposés se concentrent sur les thèmes des équations de réaction-diffusion, équations géometriques et équations de Ginzburg-Landau. On aborde à la fois des questions théoriques concernant ces équations, ainsi que des applications à des modèles en sciences sociales, écologie, physique, neurosciences et sport.

Responsables:

Luca Rossi – coordinateur (chargé de recherche CNRS, CAMS)
Amandine Aftalion (directeur de recherche CNRS, CAMS)
Henri Berestycki (directeur d’études EHESS, CAMS)
Grégoire Nadin (chargé de recherche CNRS, Université Pierre et Marie Curie)
Jean-Michel Roquejoffre (professeur de l’Université Paul Sabatier de Toulouse)
Alessandro Sarti (directeur de recherche CNRS, CAMS)
Alessandro Zilio (maîtres de conférences de l’Université Paris Diderot)

Mots-clés : ÉconomieMathématiques et sciences socialesSciencesSciences cognitives,

PROGRAMME

29-01-2018

Hirokazu Ninomiya (Meiji University)

« Entire solutions of the Allen-Cahn-Nagumo equation »

Abstract:

Propagation phenomena are often observed in many fields including dissipative situations. To characterize the universal profiles of these phenomena, traveling wave solutions and entire solutions play important roles. Here traveling wave solution is meant by a solution of a partial differential equation that propagates with a constant speed, while it maintains its shape in space, and an entire solution is a solution defined for all time.

In this talk we focus on the Allen-Cahn-Nagumo equation, which is a single reaction diffusion equation with bistable nonlinearity. One of the ways to handle more complicated propagation phenomena is to derive a method to compose the known solutions. I explain how to construct entire solutions by composing the traveling wave solutions. I also discuss the relation between traveling wave solutions and entire solutions. Especially I will introduce the zipping wave solutions and the entire solution whose level sets are approximately equidistant from any convex set as time goes to – infinity.

11-02-2018

Lenya Ryzhik (Stanford University)

« The random heat equation in dimensions three and higher »

Abstract: We consider the long time behavior of the solutions of the heat equation with a random time-dependent potential in dimensions larger than three. We show that in the long time limit, an appropriately renormalized solution converges weakly, as a Schwartz distribution, to a deterministic solution of the diffusion equation with a non-trivial effective diffusivity. We also identify the limit of the fluctuations.

This is a joint work with Y. Gu and O. Zeitouni.

23-05-2018

Alessio Porretta (Università di Roma Tor Vergata)

à 11h dans la salle 8 du 105 bd Raspail-24.
Long time behavior of mean field games

Abstract:
In this talk, based on my collaborations with P. Cardaliaguet, J-M.
Lasry and P.-L. Lions, I will discuss the long time behavior of mean field games systems in
the stable case (monotone couplings) when the dynamic takes place in the
flat torus. I will explain the main features that appeared in the study of the long
time limit: the effects of the forward-backward coupling, the ergodic behavior and
the turnpike property of the underlying control problems, the long time convergence
of the master equation. This latter step is crucial in order to fully characterize the
limit of the value function compared to what happens for a single Hamilton-Jacobi equation.