Let $\Omega\subset\mathbb R^N$ be a bounded open set with Lipschitz continuous boundary $\Gamma$. Let $\gamma>0$, $\delta\ge 0$ be real numbers and $\beta$ a nonnegative measurable function in $L^\infty(\Gamma)$. Using some suitable Carleman estimates, we show that the linear heat equation $\partial_tu - \gamma\Delta u = 0$ in $\Omega\times(0,T)$ with the non-homogeneous general dynamic boundary conditions $\partial_tu_{ \Gamma} -\delta\Delta_\Gamma u_{ \Gamma}+ \gamma\partial_{ \nu}u + \beta u_{ \Gamma} = g$ on $\Gamma\times(0,T)$ is always null controllable from the boundary for every $T>0$ and initial data $(u_0,u_{ \Gamma,0})\in L^2(\Omega)\times L^2(\Gamma)$.
Categories: math.AP