Null controllability for a heat equation with dynamic boundary conditions and drift terms

Abstract

We consider the heat equation in a bounded domain of \begin{document}$ \mathbb{R}^N $\end{document} with distributed control (supported on a small open subset) subject to dynamic boundary conditions of surface diffusion type and involving drift terms on the bulk and on the boundary. We prove that the system is null controllable at any time. The result is based on new Carleman estimates for this type of boundary conditions.