Exponential stability of the Euler-Bernoulli microbeam and thermal effect
Analysis of PDEs
2021-10-04 v1
Abstract
The main goal in this work is to prove the exponential decay of the semigroup associated with a thermoelastic system composed of an Euler-Bernoulli type equation that models the transverse oscillation of a homogeneous microbeam with axial movement and in which a viscous damping is acting. In addition, to this microbeam has been endowed with a thermal effect given by the Coleman-Gurtin model which depends essentially on past history, representing an improvement of Fourier, Cattaneo, and Green-Naghdi models. To achieve these goals, we will use mainly multiplicative techniques and standard tools of functional analysis.
Cite
@article{arxiv.2110.00187,
title = {Exponential stability of the Euler-Bernoulli microbeam and thermal effect},
author = {Roberto Díaz and Octavio Vera and Nicolás Zumelzu},
journal= {arXiv preprint arXiv:2110.00187},
year = {2021}
}