Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations

2019 ◽  
Vol 25 (1) ◽  
pp. 97-110
Author(s):  
Muhammad I. Mustafa ◽  
Mohammad Kafini
Keyword(s):  
Asymptotic Behavior ◽  
General Formula ◽  
Energy Decay ◽  
Decay Rates ◽  
Quasilinear System ◽  
Relaxation Functions ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Equations ◽  
Energy Decay Rates

Abstract In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.

scholarly journals Decay rates for solutions of a Timoshenko system with a memory condition at the boundary

2002 ◽  
Vol 7 (10) ◽  
pp. 531-546 ◽  
Author(s):  
Mauro de Lima Santos
Keyword(s):  
Asymptotic Behavior ◽  
Energy Decay ◽  
Decay Rates ◽  
Memory Condition ◽  
Timoshenko System ◽  
Relaxation Functions ◽  
Rate Of Decay ◽  
With Memory

We consider a Timoshenko system with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We prove that the energy decay with the same rate of decay of the relaxation functions, that is, the energy decays exponentially when the relaxation functions decays exponentially and polynomially when the relaxation functions decays polynomially.

scholarly journals Uniform Energy Decay Rates for the Fuzzy Viscoelastic Model with a Nonlinear Source

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fengyun Zhang
Keyword(s):  
Viscoelastic Model ◽  
Energy Decay ◽  
Decay Rates ◽  
Polynomial Form ◽  
Computational Technique ◽  
Exponential Form ◽  
Nonlinear Source ◽  
Priori Estimates ◽  
Energy Decay Rates ◽  
Mathematica Software

This paper considers the fuzzy viscoelastic model with a nonlinear source u t t + L u + ∫ 0 t g t − ζ Δ u ζ d ζ − u γ u − η Δ u t = 0 in a bounded field Ω. Under weak assumptions of the function g t , with the aid of Mathematica software, the computational technique is used to construct the auxiliary functionals and precise priori estimates. As time goes to infinity, we prove that the solution is global and energy decays to zero in two different ways: the exponential form and the polynomial form.

Blow Up of Solutions for a System of Nonlinear Viscoelastic Equations with Damping Terms in Rn

2009 ◽  
Vol 64 (3-4) ◽  
pp. 180-184
Author(s):  
Wenjun Liu ◽  
Shengqi Yub
Keyword(s):  
Initial Data ◽  
Differential Inequality ◽  
Blow Up ◽  
Coupled System ◽  
Initial Energy ◽  
Relaxation Functions ◽  
Nonlinear Viscoelastic ◽  
Linear Damping ◽  
Viscoelastic Equations ◽  
Damping And Source Terms

Abstract We consider a coupled system of nonlinear viscoelastic equations with linear damping and source terms. Under suitable conditions of the initial data and the relaxation functions, we prove a finitetime blow-up result with vanishing initial energy by using the modified energy method and a crucial lemma on differential inequality

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