Logarithmic convexity and impulsive controllability for the 1-D 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 1-D 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.

22 pages, 4 figures, 1 table

References in corpus (4)

• Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions
• The cost of approximate controllability of heat equation with dynamical boundary conditions
• An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions
• Inverse problems for general parabolic systems and application to Ornstein-Uhlenbeck equation

Cited by in corpus (1)

• Finite-time stabilization and impulse control of heat equation with dynamic boundary conditions