Seminario interdisciplinare
ore
11:15
presso Aula Seminario VIII piano
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).