scholarly journals On the viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources with variable-exponent nonlinearities

2020 ◽  
Vol 65 (4) ◽  
pp. 599-639
Author(s):  
Abita Rahmoune ◽  
Benyattou Benabderrahmane
Keyword(s):  
Decay Rate ◽  
Relaxation Function ◽  
Variable Exponent ◽  
Nonlinear Boundary ◽  
Variable Exponents ◽  
Nonlinear Feedback ◽  
Uniform Decay ◽  
Nonlinear Viscoelastic ◽  
Solution Energy ◽  
Viscoelastic Equation

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping and nonlinear boundary interior sources with variable exponents. Under appropriate assumptions, we establish a uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

Global existence and uniform decay for a nonlinear viscoelastic equation with damping

2009 ◽  
Vol 70 (9) ◽  
pp. 3090-3098 ◽  
Author(s):  
Xiaosen Han ◽  
Mingxin Wang
Keyword(s):  
Global Existence ◽  
Uniform Decay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

General decay results for a viscoelastic wave equation with a variable exponent nonlinearity

2021 ◽  
pp. 1-24
Author(s):  
Jamilu Hashim Hassan ◽  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Relaxation Function ◽  
Variable Exponent ◽  
General Decay ◽  
Viscoelastic Wave Equation ◽  
Frictional Damping ◽  
Viscoelastic Wave

In this paper we consider a viscoelastic wave equation with a very general relaxation function and nonlinear frictional damping of variable-exponent type. We give explicit and general decay results for the energy of the system depending on the decay rate of the relaxation function and the nature of the variable-exponent nonlinearity. Our results extend the existing results in the literature to the case of nonlinear frictional damping of variable-exponent type.

Global Existence and Uniform Decay for a Nonlinear Viscoelastic Equation with Damping

2009 ◽  
Vol 110 (3) ◽  
pp. 1393-1406 ◽  
Author(s):  
Jong Yeoul Park ◽  
Jum Ran Kang
Keyword(s):  
Global Existence ◽  
Uniform Decay ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equation

scholarly journals Optimal Decay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Baowei Feng ◽  
Mostafa Zahri
Keyword(s):  
Convex Function ◽  
Decay Rate ◽  
Relaxation Function ◽  
Energy Decay ◽  
Kirchhoff Plate ◽  
Nonlinear Viscoelastic ◽  
Optimal Decay ◽  
General Energy ◽  
Optimal Decay Rate

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate uttt−σΔuttt+Δ2ut−∫0tgt−sΔ2usds=divF∇ut. By assuming the minimal conditions on the relaxation function g: g′t≤ξtGgt, where G is a convex function, we establish optimal explicit and general energy decay results to the system. Our result holds for Gt=tp with the range p∈1, 2, which improves earlier decay results with the range p∈1,3/2. At last, we give some numerical illustrations and related comparisons.

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

scholarly journals Peridynamic model for nonlinear viscoelastic creep and creep rupture of Polypropylene

2019 ◽  
Vol 13 (4) ◽  
pp. 5735-5752 ◽  
Author(s):  
M. A. Azizi ◽  
A. K. Ariffin
Keyword(s):  
Internal State ◽  
Creep Behaviour ◽  
Numerical Data ◽  
Creep Rupture ◽  
Experimental Result ◽  
Viscoelastic Creep ◽  
Nonlinear Viscoelastic ◽  
Secondary Stage ◽  
Peridynamic Model ◽  
Viscoelastic Equation

This paper presents the peridynamic numerical method for nonlinear viscoelastic creep behaviour which consists of primary, secondary, tertiary creep stages and creep rupture. A nonlinear viscoelastic creep constitutive equation based on internal state variable (ISV) theory which covers four creep stages is examined. The viscoelastic equation is substituted into material parameter in the peridynamic equation to derive a new peridynamic method with two time parameters i.e. numerical time and real time. The parameters of the viscoelastic equation is analyzed and evaluated. In validating this peridynamic method, a comparison is made between numerical and experimental data. The peridynamic method for nonlinear viscoelastic creep behaviour (VE-PD) is approved by the good similarity between numerical and experimental creep strain curves with overall difference of 10.67%. The nonlinearity of experimental and numerical data is adequately similar as the error between experimental and numerical curves of secondary stage strain rate against load is 8.022%. The shapes of fractured numerical specimen show good resemblance with the experimental result as well.

scholarly journals General decay rate of a weakly dissipative viscoelastic equation with a general damping

2020 ◽  
Vol 40 (6) ◽  
pp. 647-666
Author(s):  
Khaleel Anaya ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Wide Class ◽  
Nonlinear Damping ◽  
Numerical Results ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Viscoelastic Equation

In this paper, we consider a weakly dissipative viscoelastic equation with a nonlinear damping. A general decay rate is proved for a wide class of relaxation functions. To support our theoretical findings, some numerical results are provided.

scholarly journals Existence, blow-up and exponential decay estimates for a system of nonlinear viscoelastic wave equations with nonlinear boundary conditions

2020 ◽  
Vol 19 (1) ◽  
pp. 455-492 ◽  
Author(s):  
Nguyen Thanh Long ◽  
◽  
Hoang Hai Ha ◽  
Le Thi Phuong Ngoc ◽  
Nguyen Anh Triet ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Exponential Decay ◽  
Wave Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Decay Estimates ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave
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