General and optimal decay in a memory-type Timoshenko system

2018 ◽  
Vol 30 (1) ◽  
pp. 117-145 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Jamilu Hashim Hassan
Keyword(s):  
Timoshenko System ◽  
Optimal Decay ◽  
Memory Type

DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

2012 ◽  
Vol 22 (02) ◽  
pp. 1150012 ◽  
Author(s):  
YONGQIN LIU ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Decay Estimate ◽  
Pointwise Estimate ◽  
Decay Property ◽  
Memory Term ◽  
Fourier Space ◽  
Initial Value ◽  
Timoshenko System ◽  
Frictional Dissipation ◽  
Memory Type ◽  
With Memory

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

Stability to the dissipative Reissner–Mindlin–Timoshenko acting on displacement equation

2015 ◽  
Vol 27 (2) ◽  
pp. 157-193 ◽  
Author(s):  
A. D. S. CAMPELO ◽  
D. S. ALMEIDA JÚNIOR ◽  
M. L. SANTOS
Keyword(s):  
Numerical Experiments ◽  
Transverse Displacement ◽  
Timoshenko System ◽  
Infinite Dimensional ◽  
Optimal Decay ◽  
Displacement Equation ◽  
Frictional Dissipation ◽  
Optimal Decay Rate ◽  
Exponentially Stable ◽  
Image Position

In this paper, we show that there exists a critical number that stabilises the Reissner–Mindlin–Timoshenko system with frictional dissipation acting only on the equation for the transverse displacement. We identify that the Reissner–Mindlin–Timoshenko system has two speed characteristics v12 := K/ρ1 and v22 := D/ρ2 and we show that the system is exponentially stable if only if \begin{equation*} v_{1}^{2}=v_{2}^{2}. \end{equation*}In the general case, we prove that the system is polynomially stable with optimal decay rate. Numerical experiments using finite differences are given to confirm our analytical results. Our numerical results are qualitatively in agreement with the corresponding results from dynamical in infinite dimensional.

scholarly journals A new stability result for a thermoelastic Bresse system with viscoelastic damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soh Edwin Mukiawa ◽  
Cyril Dennis Enyi ◽  
Tijani Abdulaziz Apalara
Keyword(s):  
Stability Result ◽  
Bending Moment ◽  
Decay Rates ◽  
Viscoelastic Damping ◽  
Physical Parameters ◽  
Bresse System ◽  
Solution Energy ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Weaker Conditions

AbstractWe investigate a thermoelastic Bresse system with viscoelastic damping acting on the shear force and heat conduction acting on the bending moment. We show that with weaker conditions on the relaxation function and physical parameters, the solution energy has general and optimal decay rates. Some examples are given to illustrate the findings.

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