Stabilization Results of a Piezoelectric Beams with Partial Viscous Dampings and Under Lorenz Gauge Condition

摘要

In this paper, we investigate the stabilization of a one-dimensional piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge conditions, we reformulate our system to achieve the existence and uniqueness of the solution. Next, by using General criteria of Arendt-Batty, we prove the strong stability in different cases. Finally, we prove that it is sufficient to control the stretching of the center-line of the beam in x-direction to achieve the exponential stability. Numerical results are also presented to validate our theoretical result.