The next APDE seminar will take place Monday, Nov 19, in 740 Evans from 4-5pm.
Title: Rough control for Schr\”odinger operators on 2-tori.
Abstract: I will explain how the results of Bourgain, Burq and the
speaker ’13 can be used to obtain control and observability by rough
functions and sets on 2-tori. We show that for the time dependent
Schrödinger equation, any set of positive measure can be used for
observability and controllability.
For non-empty open sets this follows from the results of Haraux ’89
and Jaffard ’90, while for sufficiently long times and rational tori
this can be deduced from the results of Jakobson ’97.