Estabilidade e controlabilidade exata para um sistema de Timoshenko com apenas um controle na fronteira

Abstract

In this dissertation, we study the stability and exact controllability of a Timoshenko system. In the first part of the work, we consider the Timoshenko system with only one boundary fractional damping. We first show that the system is strongly stable, but not uniformly stable. In the second part, we study the boundary exact controllability of the Timoshenko system with only one control. Using non-harmonic analysis arguments and the Hilbert Uniqueness Method (HUM), we prove that the system is exactly controllable in appropriate spaces.