R. Lecaros, R. Morales, A. Pérez, S. Zamorano (2023) Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions, Differ. Equ., Vol. 365, pp. 832-881, https://doi.org/10.1016/j.jde.2023.05.014
Abstract. We consider a fully-discrete approximation of a 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding adjoint system. This is conducted using a suitable Carleman estimate for such models where the discrete parameters h and Δt are connected to one of the large Carleman parameters.