The influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization

2021/02/28 by Mohammad Akil, Akil, Mohammad, Haidar Badawi +1
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2103.00628

openalex publication_date 2021/02/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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 and only 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 t^-1 or t^-(1)/(2).

Related

• On the stability of the Bresse system with frictional damping
• Polynomial and non exponential stability of a weak dissipative Bresse system
• Polynomial stabilization of non-smooth direct/indirect elastic/viscoelastic damping problem involving Bresse system
• The lack of exponential stability of a Bresse system subjected only to two dampings
• Locally internal stability of weakly elastic Bresse system