On the stabilization of a flexible structure via a nonlinear delayed boundary control

Abstract

<p style='text-indent:20px;'>The main concern of this article is to investigate the stabilization problem of a flexible structure with one dynamical boundary condition subject to two nonlinearities in the proposed boundary control. Specifically, the first nonlinearity is related to the velocity term, while the second one arises from the delayed term. Despite such a situation, it is shown that the system has a global solution by means of semigroups theory of nonlinear operators. More importantly, we prove that the system energy decays. An estimate of the decay rate of the energy is explicitly provided depending on the type of the nonlinearities.</p>