Abstract

In this talk, I first review some known results on the observability inequality from measurable sets for the heat equation on bounded domains, and show its applications in optimization problems. Then I will talk about some recent results on observability estimates from thick sets for the heat equation in R^N. Finally, I will consider the null controllability from equi-distributed sets for the heat equation with bounded potentials, as well as for the semi-linear heat equation in R^N.