Seminari del Dipartimento di Matematica

Seminario del 2018

Maciej Zworski (Berkeley University)

Control and observability on tori (part 2)

nell'ambito della serie: TOPICS IN MATHEMATICS 2017/2018

SEMINARIO INTERDISCIPLINARE

I will use time dependent Schroedinger equation on the two dimensional torus as a ``laboratory" for describing control and observability for time dependent PDE. The plan of the lectures is 1. General description of the problem and Lions's argument for the equivalence of observability and control. 2. Introduction to semiclassical methods and defect measures. 3. Control by non-empty open sets on tori (a proof of now classical results of Haraux, Jaffard and Komornik using defect measures). 4. A review of modern advances: control by sets of positive Lebesgue measure (Bourgain--Burq--Z, Burq--Z), control on discs (Anantharaman--Leautaud--Macia), control by non-empty open sets on hyperbolic surfaces (Bourgain--Dyatlov, Dyatlov--Jin, Jin).