scholarly journals General decay estimates for a Cauchy viscoelastic wave problem

2014 ◽  
Vol 13 (4) ◽  
pp. 1541-1551 ◽  
Author(s):  
Belkacem Said-Houari ◽  
Salim A. Messaoudi
Keyword(s):  
General Decay ◽  
Decay Estimates ◽  
Wave Problem ◽  
Viscoelastic Wave

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.

scholarly journals Existence and general decay of Balakrishnan-Taylor viscoelastic equation with nonlinear frictional damping and logarithmic source term

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Al-Gharabli ◽  
Mohamed Balegh ◽  
Baowei Feng ◽  
Zayd Hajjej ◽  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Convex Functions ◽  
General Type ◽  
Source Term ◽  
General Decay ◽  
General Decay Rate ◽  
Relaxation Functions ◽  
Frictional Damping ◽  
Viscoelastic Wave ◽  
Viscoelastic Equation

<p style='text-indent:20px;'>In this paper, we consider a Balakrishnan-Taylor viscoelastic wave equation with nonlinear frictional damping and logarithmic source term. By assuming a more general type of relaxation functions, we establish explicit and general decay rate results, using the multiplier method and some properties of the convex functions. This result is new and generalizes earlier results in the literature.</p>

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