Today December 3rd our Postdoctoral member Jon Asier Bárcena Petisco talked about “Some recent results about the controllability of the heat equation“ at the event 3rd. BYMAT – Bringing Young Mathematicians Together organized by the Polytechnic University of Valencia (Universidad Politécnica de Valencia), Spain.
Abstract. The heat equation is the most basic parabolic PDE. Its null controllability was proved in the90s for allC2domains by Fursikov and Imanuvilov. However, this is not the end of the story: there are still plenty of interesting questions about the controllability of the heat equation. In this talk we discuss briefly some of them and present recent progress in answering them. A first one is to determine if the heat equation is indeed null controllable in all Lipschitz domains. A second one is to determine the evolution of the cost of the controllability when the diffusion vanishes and there is a transport term. In particular, we focus on the heat equation with Robin and mixed boundary conditions. A third and last one is the controllability of the stochastic heat equation with a random diffusion.