Internal null controllability for the one-dimensional heat equation with dynamic boundary conditions

Abstract

The primary focus of this paper is to establish the internal null controllability for the one-dimensional heat equation featuring dynamic boundary conditions. This achievement is realized by introducing a new Carleman estimate and an observability inequality for the corresponding backward system. In conclusion, the paper includes a set of numerical experiments that serve to confirm the validity of the theoretical findings and underscore the effectiveness of the designed control with a minimal L2-norm.