Comportamento assintótico para sistemas de Timoshenko com dissipações na fronteira : boa colocação e estabilidade

Abstract

In this work, we will analyze the existence, uniqueness and asymptotic behavior for a Timoshenko System with distinct types of dissipation, employing the technique of semigroups of linear operators. Throughout the work, we will study well-posedness for three types of dissipation on the boundary and we will impose conditions on the system to ensure exponential stability. For existence and uniqueness, we will take an approach by studying the system as an Abstract Cauchy problem in the semigroup theory of operators, making use of tools such as: Sobolev spaces, Hilbert spaces and functional analysis, this for each case studied. For the exponential stability of the solutions of the Abstract Cauchy Problem, we will use different techniques included: immersions in Sobolev spaces, spectral theory of linear operators and some classical inequalities of functional analysis.