scholarly journals Asymptotics for some nonlinear damped wave equation: finite time convergence versus exponential decay results

2007 ◽  
Vol 24 (6) ◽  
pp. 1009-1028 ◽  
Author(s):  
B. Baji ◽  
A. Cabot ◽  
J.I. Díaz
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Finite Time ◽  
Damped Wave Equation ◽  
Finite Time Convergence ◽  
Nonlinear Damped Wave Equation

Global solutions and finite time blow-up for fourth order nonlinear damped wave equation

2018 ◽  
Vol 59 (6) ◽  
pp. 061503 ◽  
Author(s):  
Runzhang Xu ◽  
Xingchang Wang ◽  
Yanbing Yang ◽  
Shaohua Chen
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation

scholarly journals Exponential decay for the damped wave equation in unbounded domains

2016 ◽  
Vol 18 (06) ◽  
pp. 1650012 ◽  
Author(s):  
Nicolas Burq ◽  
Romain Joly
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Exponential Decay ◽  
Unbounded Domain ◽  
Unbounded Domains ◽  
Geometric Control ◽  
Damped Wave Equation ◽  
Logarithmic Decay ◽  
And Control

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilization and control.

scholarly journals Nonlinear damped wave equation: Existence and blow-up

2017 ◽  
Vol 74 (12) ◽  
pp. 3024-3041 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Ala A. Talahmeh ◽  
Jamal H. Al-Smail
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Damped Wave Equation ◽  
Nonlinear Damped Wave Equation
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