scholarly journals On a Class of Nonlinear Viscoelastic Kirchhoff Plates: Well-Posedness and General Decay Rates

2015 ◽  
Vol 73 (1) ◽  
pp. 165-194 ◽  
Author(s):  
M. A. Jorge Silva ◽  
J. E. Muñoz Rivera ◽  
R. Racke
Keyword(s):  
Decay Rates ◽  
General Decay ◽  
Well Posedness ◽  
Kirchhoff Plates ◽  
Nonlinear Viscoelastic

scholarly journals Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdelbaki Choucha ◽  
Salah Boulaaras
Keyword(s):  
Asymptotic Behavior ◽  
Decay Rate ◽  
Energy Method ◽  
Distributed Delay ◽  
Type Equation ◽  
General Decay ◽  
Kirchhoff Equation ◽  
General Decay Rate ◽  
Kirchhoff Type ◽  
Nonlinear Viscoelastic

AbstractA nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

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 General decay of solutions of a thermoelastic Bresse system with viscoelastic boundary conditions

2021 ◽  
Vol 39 (6) ◽  
pp. 157-182
Author(s):  
Ammar Khemmoudj
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Decay Rates ◽  
General Decay ◽  
Polynomial Decay ◽  
Relaxation Functions ◽  
Bresse System ◽  
Decay Of Solutions ◽  
Special Cases

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory eect is strong enough to produce a general decay results. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

The Importance of the Compatibility of Nonlinear Constitutive Theories With Their Linear Counterparts

2006 ◽  
Vol 74 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Ramon Quintanilla ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problem ◽  
Mechanical Model ◽  
Linear Viscoelasticity ◽  
Special Class ◽  
Boundary Value ◽  
Well Posedness ◽  
Constitutive Theories ◽  
Nonlinear Viscoelastic ◽  
Simple Boundary ◽  
Nonlinear Viscoelastic Materials

We show, by considering a special class of nonlinear viscoelastic materials, that consistency of a mechanical model with classical linear viscoelasticity, may be a fundamental condition to ensure a mathematical and physical well-posedness behavior. To illustrate our arguments we use a rectilinear class of shear motions that we investigate in the static and quasistatic case in the framework of a simple boundary value problem and the classical recovery phenomenon.

General decay in a Timoshenko-type system with thermoelasticity with second sound

2015 ◽  
Vol 4 (4) ◽  
pp. 263-284 ◽  
Author(s):  
Mohamed Ali Ayadi ◽  
Ahmed Bchatnia ◽  
Makram Hamouda ◽  
Salim Messaoudi
Keyword(s):  
Group Theory ◽  
Type System ◽  
General Decay ◽  
Regularity Of Solutions ◽  
Well Posedness ◽  
Second Sound ◽  
Semi Group ◽  
Stability Number ◽  
Timoshenko System ◽  
Relaxation Functions

AbstractIn this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

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