Remark on stabilization of second order evolution equations by unbounded dynamic feedbacks and applications

TL;DR

This paper investigates the stabilization of second order evolution equations using unbounded dynamic feedbacks, demonstrating how observability of the undamped system leads to decay estimates for the damped system under certain regularity conditions.

Contribution

It establishes a link between observability properties and decay rates for second order evolution equations with unbounded feedbacks, extending stability analysis methods.

Findings

Observability implies decay estimates for damped systems.

Both uniform and non-uniform decay properties are analyzed.

Results apply under specific regularity assumptions.

Abstract

In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.