Some recent results about the controllability of the heat equation
Speaker: Jon Asier Bárcena-Petisco
Affiliation: LJLL- Sorbonne Université, France
Abstract: The heat equation is the most basic parabolic PDE. Its null controllability was proved in the 90s for all C 2 domains 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 first-order 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.