scholarly journals Uniform Decay of Solutions for a Nonlinear Viscoelastic Wave Equation with Boundary Dissipation

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Shun-Tang Wu ◽  
Hsueh-Fang Chen
Keyword(s):  
Wave Equation ◽  
Uniform Decay ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Decay Of Solutions ◽  
Viscoelastic Wave ◽  
Boundary Dissipation

scholarly journals On the blow-up of the Cauchy problem of higher-order nonlinear viscoelastic wave equation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Kafini
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Blow Up ◽  
Initial Energy ◽  
Higher Order ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave ◽  
The Cauchy Problem ◽  
Whole Space

<p style='text-indent:20px;'>In this paper we consider the Cauchy problem for a higher-order viscoelastic wave equation with finite memory and nonlinear logarithmic source term. Under certain conditions on the initial data with negative initial energy and with certain class of relaxation functions, we prove a finite-time blow-up result in the whole space. Moreover, the blow-up time is estimated explicitly. The upper bound and the lower bound for the blow up time are estimated.</p>

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