Exponential stability of a damped beam-string-beam transmission problem
Date
2022-04-13
Authors
Barraza Martinez, Bienvenido
Hernandez Monzon, Jairo
Vergara Rolong, Gustavo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with a frictionally damped string by transmission conditions. We show that for this structure, the dissipation produced by the frictional part is strong enough to produce exponential decay of the solution no matter how small is its size. For the exponential stability in the damped-damped-damped situation we use energy method. For the undamped-damped-undamped situation we use a frequency domain method from semigroups theory, which combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. Additionally, we show that the solution first defined by the weak formulation has higher Sobolev space regularity.
Description
Keywords
Exponential stability, Transmission problems, Frictional damping, Beam-string equations
Citation
Barraza Martínez, B., Hernández Monzón, J., & Vergara Rolong, G. (2022). Exponential stability of a damped beam-string-beam transmission problem. <i>Electronic Journal of Differential Equations, 2022</i>(30), pp. 1-19.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.