Finite-Time Stabilization and Impulse Control of Heat Equation with Dynamic Boundary Conditions

In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in bounded smooth domain. Using recent approach based on finite-time stabilization, show that system is null controllable at any positive time via controls supported nonempty open subset physical Furthermore, infer an explicit estimate for exponential decay solution. The proof main result combines logarithmic convexity and some spectral properties associated to conditions. our setting, nature equations, which couple intern-boundary phenomena, makes it necessary go into quite sophisticated estimates incorporating several terms.