Introdução às bases de Riesz e aplicações na estabilização fronteira de problemas de vigas - Silva, Alessandro Fernandes (2022)
In this work we will study a method that is possible to generate one-dimensional Riesz bases, beam equation type under boundary controls or point feedback. The generation of the Riesz base naturally results in exponential stability and the growth condition determined by the spectrum. We will study two beam problems that will be represented by evolution equations, in them we will investigate the asymptotic behavior and the analyticity of the solutions. Our main objective is to present the necessary and sufficient conditions to obtain an exponential stability of the corresponding semigroup.