Open AccessThe influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization
Author(s) -
Mohammad Akil,
Haidar Badawi
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2022004
Subject(s) - dirichlet boundary condition , mathematics , boundary (topology) , mathematical analysis , domain (mathematical analysis) , displacement (psychology) , stability (learning theory) , energy (signal processing) , physics , computer science , psychology , machine learning , psychotherapist , statistics
In this paper, we investigate the stabilization of a linear Bresse system with one singular local frictional damping acting in the longitudinal displacement, under fully Dirichlet boundary conditions. First, we prove the strong stability of our system. Next, using a frequency domain approach combined with the multiplier method, we establish the exponential stability of the solution if the three waves have the same speed of propagation. On the contrary, we prove that the energy of our system decays polynomially with rates \begin{document}$ t^{-1} $\end{document} or \begin{document}$ t^{-\frac{1}{2}} $\end{document} .