Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions

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.