Guest Lecture : Charles Collot

Dynamics around self-similar solutions in evolution PDEs, with the example of a soliton in 1d nonlinear Schrodinger equations

Charles Collot est professeur au laboratoire AGM, CYU

In the area of nonlinear evolution partial differential equations, one research direction has become a major one over the last 30 years: studying the role played by self-similar solutions in the dynamics. Self-similar solutions are those that keep the same shape over time up to renormalisation, like stationary states, traveling waves, etc... The first part of the talk will introduce the soliton resolution conjecture, which states that for many PDEs, in certain contexts, general solutions are expected to decompose asymptotically in time into a sum of such self-similar solutions plus a lower order radiation. I will then illustrate this asymptotic description with some results I obtained, including examples of solutions for which these self-similar solutions produce remarkable concentration and propagation effects. The last part will focus on the example of 1D nonlinear Schrodinger equations. I will present a recent work with P. Germain (Imperial College, London) in which we establish the asymptotic stability of traveling waves through long-range scattering for the radiation.


Date : 19 décembre 2023 de 14h00 à 15h30

La guest lecture hybride est organisée en présence dans la salle de réunion H008 de la MIR à Neuville-sur-Oise et à distance sur Zoom.

Pour participer à la guest lecture à distance, connectez-vous sur Zoom : https://cyu-fr.zoom.us/j/93689087766

ID réunion : 936 8908 7766

La vidéo sera publiée sur la chaîne YouTube de CY AS

Crédit photographique : Archives of the Mathematisches Forschungsinstitut Oberwolfach