Blow up and global existence in a nonlinear viscoelastic wave equation

2003 ◽  
Vol 260 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Salim A. Messaoudi
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Blow Up ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave

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>

scholarly journals Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping

2018 ◽  
Vol 3 (4) ◽  
pp. 514-523
Author(s):  
Xiaoming Peng ◽  
◽  
Xiaoxiao Zheng ◽  
Yadong Shang ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Lower Bounds ◽  
Blow Up ◽  
Strong Damping ◽  
Viscoelastic Wave Equation ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Wave
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