A sharper decay rate for a viscoelastic wave equation with power nonlinearity

2019 ◽  
Vol 43 (3) ◽  
pp. 1138-1144 ◽  
Author(s):  
Tosiya Miyasita ◽  
Khaled Zennir
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Power Nonlinearity ◽  
Viscoelastic Wave Equation ◽  
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.

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