Limites assintóticos e estabilidade para o sistema de Mindlin-Timoshenko.

Abstract

This thesis is concerned with the dynamics of Mindlin-Timoshenko system for beams and plates. We study issues relating to the asymptotic limit in relation to the parameters, decay rates and the existence of controls that lead to our solution of the system from an initial state prescribed to a final desired state at a given time positive. In the context of asymptotic limit, as the main result, we present a positive response to the conjecture made by Lagnese and Lions in 1988, where the Von-Kármán model is obtained as singular limit when k tends to infinity, the Mindlin-Timoshenko system. Introducing appropriate damping mechanisms (internal and boundary), we also show that the energy of solutions for the Mindlin-Timoshenko system has decay properties exponential and polynomial, with respect to the parameters.