General decay rates for one-dimensional porous-elastic system with memory: The case of non-equal wave speeds

2020 ◽  
Vol 482 (2) ◽  
pp. 123552
Author(s):  
Wenjun Liu ◽  
Dongqin Chen ◽  
Salim A. Messaoudi
Keyword(s):  
Elastic System ◽  
Decay Rates ◽  
General Decay ◽  
Wave Speeds ◽  
One Dimensional ◽  
With Memory

scholarly journals Boundary Stabilization of Memory Type for the Porous-Thermo-Elasticity System

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Abdelaziz Soufyane ◽  
Mounir Afilal ◽  
Mama Chacha
Keyword(s):  
Elastic System ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Boundary Stabilization ◽  
One Dimensional ◽  
Elasticity System ◽  
Special Cases ◽  
Memory Type ◽  
The One

We consider the one-dimensional viscoelastic Porous-Thermo-Elastic system. We establish a general decay results. The usual exponential and polynomial decay rates are only special cases.

Decay of solutions for a one-dimensional porous elasticity system with memory: the case of non-equal wave speeds

2018 ◽  
Vol 24 (8) ◽  
pp. 2361-2373 ◽  
Author(s):  
Baowei Feng ◽  
Mingyang Yin
Keyword(s):  
Point Of View ◽  
General Decay ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elasticity System ◽  
Decay Of Solutions ◽  
With Memory

In previous work, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations. In this paper, we extend the result to the case of non-equal wave speeds, which is more realistic from the physics point of view.

scholarly journals General Decay of Solutions in One-Dimensional Porous-Elastic with Memory and Distributed Delay Term

2021 ◽  
Vol 52 ◽  
Author(s):  
Abdelbaki Choucha ◽  
Djamel Ouchenane ◽  
Khaled Zennir
Keyword(s):  
Energy Method ◽  
Elastic System ◽  
Distributed Delay ◽  
General Decay ◽  
Lyapunov Functionals ◽  
One Dimensional ◽  
Delay Term ◽  
Decay Of Solutions ◽  
With Memory

As a continuity to the study by T. A. Apalarain[3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1.

scholarly journals General Decay Rates for a Laminated Beam with Memory

2019 ◽  
Vol 23 (5) ◽  
pp. 1227-1252 ◽  
Author(s):  
Zhijing Chen ◽  
Wenjun Liu ◽  
Dongqin Chen
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Laminated Beam ◽  
With Memory

scholarly journals On the Stabilization for Laminated Beam with Infinite Memory and Different Speeds of Wave Propagation

2017 ◽  
Author(s):  
Gang Li ◽  
Xiangyu Kong
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Boundary Control ◽  
Rotation Angle ◽  
General Decay ◽  
Laminated Beam ◽  
Wave Speeds ◽  
Infinite Memory ◽  
One Dimensional ◽  
Order Energy

In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equations 193: 1-45, 2012) and the second-order energy.

scholarly journals General decay of the double dispersive wave equation with memory and source terms

2021 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Bounded Domain ◽  
Global Solutions ◽  
Decay Rates ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
T Tau ◽  
With Memory ◽  
Dispersive Wave Equation

The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u \) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.

General decay of porous elastic system with thermo-viscoelastic damping

2021 ◽  
Vol 9 (1) ◽  
pp. 31-43
Author(s):  
F. Djellali ◽  
◽  
S. Labidi ◽  
F. Taallah ◽  
◽  
...  
Keyword(s):  
Heat Flux ◽  
Elastic System ◽  
General Decay ◽  
Viscoelastic Damping ◽  
Stability Number ◽  
Memory Kernel ◽  
One Dimensional

In this work, we consider a one-dimensional porous thermoelastic system, where the heat flux used is introduced by Green and Naghdi theories. We establish a general decay result depending on the memory kernel and a new introduced stability number.

scholarly journals GENERAL DECAY OF SOLUTION FOR A POROUS-ELASTIC SYSTEM WITH WEAK NONLINEAR DISSIPATION

2018 ◽  
Vol 05 (01) ◽  
pp. 9-23
Author(s):  
SEBASTIAO M. S. CORDEIRO ◽  
MAURO L. SANTOS ◽  
CARLOS A. RAPOSO
Keyword(s):  
Elastic System ◽  
General Decay ◽  
Nonlinear Dissipation

scholarly journals One dimensional quantum walks with memory

2010 ◽  
Vol 10 (5&6) ◽  
pp. 509-524
Author(s):  
M. Mc Gettrick
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Walks ◽  
One Dimensional ◽  
With Memory ◽  
Previous Step

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of one previous step. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

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