Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings
Analysis of PDEs
2022-07-04 v1
Abstract
In this paper, we investigate the stabilization of a one-dimensional Lorenz 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.
Cite
@article{arxiv.2207.00488,
title = {Stabilization results of a Lorenz piezoelectric beam with partial viscous dampings},
author = {Mohammad Akil and Abdelaziz Soufyane and Youssef Belhamadia},
journal= {arXiv preprint arXiv:2207.00488},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2102.07538 by other authors