Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions

Abstract

Abstract In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for the one-dimensional heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.