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

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.

Impulse null approximate controllability for heat equation with dynamic boundary conditions

“…It should be pointed out that this method is a new approach to steer the solution to zero using impulse control as a stabilizer in finite time. Recently, in [6][7][8] the authors have established new results of impulse controllability for a general type of dynamic boundary conditions which introduce mathematical issues that require sophisticated estimates due to the boundary terms. We refer to the seminal paper [12] for more details on the non-impulsive control case.…”