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

Next Thursday January 18, 2023:

Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions
Speaker: Sebastián Zamorano Aliaga
Affiliation: University of Santiago of Chile

Abstract. In this talk, 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 $\Delta t$ are connected to one of the large Carleman parameters. At the end, we will present a non-exhaustive list of open problems and perspectives in the field.