Stabilization Results of a Piezoelectric Beams with Partial Viscous Dampings and Under Lorenz Gauge Condition
Résumé
In this paper, we investigate the stabilization of a one-dimensional piezoelectric (Stretching system) with partial viscous dampings. First, by using Lorenz gauge con- ditions, 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 stabil- ity 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.