Null Controllability of an Abstract Riesz-spectral Boundary Control Systems

This paper addresses the null controllability of an abstract boundary control systems in Hilbert spaces where the system operator is of Riesz type. Consequently, this document establishes a criterion for null controllability in such systems based on initial data, utilizing the moment problem. Furthermore, this criterion is formulated by employing a null controllability criterion that is applicable to a corresponding linear system with internal control. Finally, we apply our approach to the heat equation and the Mullins equation, demonstrating the practicality of our methodology.