scholarly journals Asymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density

2005 ◽  
Vol 2005 (10) ◽  
pp. 1497-1506 ◽  
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Asymptotic Behavior ◽  
Relaxation Function ◽  
Viscoelastic Problem ◽  
Material Density ◽  
Nonlinear Viscoelastic ◽  
Weaker Conditions ◽  
Uniformly Bounded

We consider a nonlinear viscoelastic problem and prove that the solutions are uniformly bounded and decay exponentially to zero as time goes to infinity. This is established under weaker conditions on the relaxation function than the usually used ones. In particular, we remove the assumptions on the derivative of the kernel. In fact, our kernels are not necessarily differentiable.

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 Jonscher indices for dielectric materials

2019 ◽  
Vol 09 (06) ◽  
pp. 1950046
Author(s):  
C. L. Wang
Keyword(s):  
Experimental Data ◽  
Asymptotic Behavior ◽  
Dielectric Relaxation ◽  
Time Domain ◽  
Dielectric Response ◽  
Relaxation Function ◽  
Dielectric Materials ◽  
Dielectric Response Function ◽  
Barium Stannate ◽  
Two Parameters

Two parameters are proposed as Jonscher indices, named after A. K. Jonscher for his pioneering contribution to the universal dielectric relaxation law. Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices. Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.

scholarly journals Global Nonexistence for a Nonlinear Viscoelastic Equation with Nonlinear Damping and Velocity-Dependent Material Density

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Jian Dang ◽  
Qingying Hu ◽  
Hongwei Zhang
Keyword(s):  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Energy ◽  
Material Density ◽  
Nonexistence Result ◽  
Nonlinear Viscoelastic ◽  
Global Nonexistence ◽  
Viscoelastic Equation

We consider the initial boundary value problem of a nonlinear viscoelastic equation of Kirchhoff-type with nonlinear damping and velocity-dependent material density. We establish a nonexistence result of global solutions with positive initial energy and negative initial energy, respectively.

scholarly journals On Asymptotic Behavior and Blow-Up of Solutions for a Nonlinear Viscoelastic Petrovsky Equation with Positive Initial Energy

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Gang Li ◽  
Yun Sun ◽  
Wenjun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Positive Initial Energy ◽  
Nonlinear Viscoelastic ◽  
Petrovsky Equation ◽  
Initial Boundary Value

This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equationutt+Δ2u−∫0tgt−τΔ2ux,τdτ−Δut−Δutt+utm−1ut=up−1u. Under certain conditions ongand the assumption thatm<p, we establish some asymptotic behavior and blow-up results for solutions with positive initial energy.

scholarly journals Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Anyin Xia ◽  
Mingshu Fan ◽  
Shan Li
Keyword(s):  
Electrical Resistivity ◽  
Asymptotic Behavior ◽  
Ohmic Heating ◽  
The Other ◽  
Dimensionless Temperature ◽  
Nonlocal Term ◽  
Unique Equilibrium ◽  
Heating Model ◽  
Current Flows ◽  
Uniformly Bounded

The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal termut=urr+ur/r+f(u)/(a+2πb∫01‍f(u)rdr)2,for  0<r<1,  t>0,u1,t=u′(0,t)=0,for  t>0,  ur,0=u0r,  for  0≤r≤1. The model prescribes the dimensionless temperature when the electric current flows through two conductors, subject to a fixed potential difference. One of the electrical resistivity of the axis-symmetric conductor depends on the temperature and the other one remains constant. The main results show that the temperature remains uniformly bounded for the generally decreasing functionf(s), and the global solution of the problem converges asymptotically to the unique equilibrium.

A Correspondence Principle for Free Vibrations of a Viscoelastic Solid

1966 ◽  
Vol 33 (4) ◽  
pp. 924-926 ◽  
Author(s):  
G. M. C. Fisher ◽  
M. J. Leitman
Keyword(s):  
Mode Shape ◽  
Relaxation Function ◽  
Correspondence Principle ◽  
Free Vibrations ◽  
Elastic Problem ◽  
Restricted Class ◽  
Viscoelastic Solid ◽  
Viscoelastic Problem ◽  
Linearized Theory ◽  
Theory Of Viscoelasticity

A correspondence principle for free vibrations in the classical linearized theory of viscoelasticity is established. It is shown that, for motions which are either irrotational or solenoidal, there is always an associated elastic problem with the following properties: (a) Every mode shape for the viscoelastic problem is also a mode shape for the elastic problem; and (b) the viscoelastic frequencies can, in principle, be calculated from a knowledge of the elastic spectrum and the relevant relaxation function. It is further shown that, in general, for motions which are neither irrotational nor solenoidal, this correspondence exists only for the restricted class of viscoelastic materials for which the behavior depends essentially upon one relaxation function. The paper concludes with the observation that the correspondence also exists for those approximate theories in which there appears only one relaxation function.

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