scholarly journals The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system

2014 ◽  
Vol 3 (4) ◽  
pp. 713-738 ◽  
Author(s):  
Abdelaziz Soufyane ◽  
◽  
Belkacem Said-Houari
Keyword(s):  
Decay Rate ◽  
Wave Speeds ◽  
Bresse System ◽  
Frictional Damping

scholarly journals The optimal decay rate for a weak dissipative Bresse system

2012 ◽  
Vol 25 (3) ◽  
pp. 600-604 ◽  
Author(s):  
Luci Harue Fatori ◽  
Rodrigo Nunes Monteiro
Keyword(s):  
Decay Rate ◽  
Bresse System ◽  
Optimal Decay ◽  
Optimal Decay Rate

General decay results for a viscoelastic wave equation with a variable exponent nonlinearity

2021 ◽  
pp. 1-24
Author(s):  
Jamilu Hashim Hassan ◽  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Relaxation Function ◽  
Variable Exponent ◽  
General Decay ◽  
Viscoelastic Wave Equation ◽  
Frictional Damping ◽  
Viscoelastic Wave

In this paper we consider a viscoelastic wave equation with a very general relaxation function and nonlinear frictional damping of variable-exponent type. We give explicit and general decay results for the energy of the system depending on the decay rate of the relaxation function and the nature of the variable-exponent nonlinearity. Our results extend the existing results in the literature to the case of nonlinear frictional damping of variable-exponent type.

The asymptotic behavior of the Bresse–Cattaneo system

2016 ◽  
Vol 18 (04) ◽  
pp. 1550045 ◽  
Author(s):  
Belkacem Said-Houari ◽  
Taklit Hamadouche
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Decay Rate ◽  
Stability Number ◽  
Timoshenko System ◽  
Decay Properties ◽  
Bresse System ◽  
Whole Space ◽  
The Stability ◽  
The One

In this paper, we investigate the decay properties of the Bresse–Cattaneo system in the whole space. We show that the coupling of the Bresse system with the heat conduction of the Cattaneo theory leads to a loss of regularity of the solution and we prove that the decay rate of the solution is very slow. In fact, we show that the [Formula: see text]-norm of the solution decays with the rate of [Formula: see text]. The behavior of solutions depends on a certain number [Formula: see text] (which is the same stability number for the Timoshenko–Cattaneo system [Damping by heat conduction in the Timoshenko system: Fourier and Cattaneo are the same, J. Differential Equations 255(4) (2013) 611–632; The stability number of the Timoshenko system with second sound, J. Differential Equations 253(9) (2012) 2715–2733]) which is a function of the parameters of the system. In addition, we show that we obtain the same decay rate as the one of the solution for the Bresse–Fourier model [The Bresse system in thermoelasticity, to appear in Math. Methods Appl. Sci.].

scholarly journals Exponential decay rate of the energy of a Timoshenko beam with locally distributed feedback

2002 ◽  
Vol 44 (2) ◽  
pp. 205-220 ◽  
Author(s):  
Dong-Hua Shi ◽  
De-Xing Feng
Keyword(s):  
Decay Rate ◽  
Exponential Decay ◽  
Timoshenko Beam ◽  
Closed Loop ◽  
Expansion Method ◽  
Closed Loop System ◽  
Wave Speeds ◽  
Exponential Decay Rate ◽  
Distributed Controls ◽  
Asymptotic Expansion Method

AbstractThe problem of the energy exponential decay rate of a Timoshenko beam with locally distributed controls is investigated. Consider the case in which the beam is nonuniform and the two wave speeds are different. Then, using Huang's theorem and Birkhoff's asymptotic expansion method, it is shown that, under some locally distributed controls, the energy exponential decay rate is identical to the supremum of the real part of the spectrum of the closed loop system. Furthermore, explicit asymptotic locations of eigenfrequencies are derived.

On the decay rate of solutions of the Bresse system with Gurtin–Pipkin thermal law

2017 ◽  
Vol 103 (1-2) ◽  
pp. 1-32 ◽  
Author(s):  
Maisa Khader ◽  
Belkacem Said-Houari
Keyword(s):  
Decay Rate ◽  
Bresse System
Sign in / Sign up

Export Citation Format

Share Document