scholarly journals Uniform stabilization for the transmission problem of the Timoshenko system with memory

2010 ◽  
Vol 369 (1) ◽  
pp. 323-345 ◽  
Author(s):  
Margareth S. Alves ◽  
Carlos Alberto Raposo ◽  
Jaime E. Muñoz Rivera ◽  
Mauricio Sepúlveda ◽  
Octavio Vera Villagrán
Keyword(s):  
Transmission Problem ◽  
Uniform Stabilization ◽  
Timoshenko System ◽  
With Memory

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.

scholarly journals A new perspective of exponential stability for Timoshenko systems under history and thermal effects1

2021 ◽  
pp. 1-32
Author(s):  
Marcio A. Jorge Silva ◽  
Sandro B. Pinheiro
Keyword(s):  
Exponential Stability ◽  
Thermal Effects ◽  
Viscoelastic Problem ◽  
Timoshenko System ◽  
Uniform Exponential Stability ◽  
The Subject ◽  
New Perspective ◽  
The Stability ◽  
Timoshenko Systems ◽  
With Memory

We address a Timoshenko system with memory in the history context and thermoelasticity of type III for heat conduction. Our main goal is to prove its uniform (exponential) stability by illustrating carefully the sensitivity of the heat and history couplings on the Timoshenko system. This investigation contrasts previous insights on the subject and promotes a new perspective with respect to the stability of the thermo-viscoelastic problem carried out, by combining the whole strength of history and thermal effects.

scholarly journals Property of growth determined by the spectrum of operator associated to Timoshenko system with memory

2019 ◽  
Vol 23 (1) ◽  
pp. 75-96
Author(s):  
Ronaldo Ribeiro-Alves ◽  
Jaime Muñoz-Rivera ◽  
Carlos Raposo
Keyword(s):  
Timoshenko System ◽  
With Memory
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