# Talk by Julien Royer

On April 12th, 2023, Julien Royer (Université Paul Sabatier, Institut de Mathématiques de Toulouse) gave a talk about **"Local energy decay for the wave and Schrödinger equations****" **as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.

## Abstract

In this talk we will discuss a recent result about the local energy decay for the Schrödinger equation in an asymptotically Euclidean setting. More precisely, we will focus on the contribution of low frequency, whose behavior is given by the resolvent of the Laplacian near 0. After a review of some results about the damped wave equation, we will see how some ideas developed to deal with a non-selfadjoint operator can be used to improve what is known in a purely conservative setting.