Impulse controllability for the heat equation with inverse square potential and dynamic boundary conditions

Abstract

Abstract In this paper, we investigate the null approximate impulse controllability of the heat equation with an inverse square potential subject to dynamic boundary conditions in the ball $B(0, R_{0})$ of radius $R_{0}=\left (\frac{4}{3}\right )^{\frac{3}{2}}$. To that purpose, we use the Carleman commutator approach to show a logarithmic convexity estimate traducing an observability inequality at one instant of time.