Existence and non-existence of global solutions of a non-local wave equation

2004 ◽  
Vol 27 (15) ◽  
pp. 1747-1754 ◽  
Author(s):  
Azmy S. Ackleh ◽  
Keng Deng
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Local Wave ◽  
Non Local

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 Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Daewook Kim ◽  
Dojin Kim ◽  
Keum-Shik Hong ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Existence And Uniqueness ◽  
Global Solutions ◽  
Growth Conditions ◽  
Decay Rates ◽  
Decay Estimates ◽  
Nonlinear Dissipation ◽  
Kirchhoff Type ◽  
Type Wave ◽  
Energy Decay Rates

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form under suitable assumptions on . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipationg. Lastly, numerical simulations in order to verify the analytical results are given.

scholarly journals On global solutions to a nonlinear Alfvén wave equation

1995 ◽  
Vol 62 (2) ◽  
pp. 155-172
Author(s):  
XS. Feng ◽  
F. Wei
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Alfven Wave

scholarly journals Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation

1993 ◽  
Vol 15 (15) ◽  
pp. 17
Author(s):  
Eleni Bisognin
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Exponential Decay ◽  
Lipschitz Function ◽  
Global Solutions ◽  
Work Study ◽  
Carrier Wave ◽  
Decay Of Solutions ◽  
Lipschitz Perturbation

In this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equationu" - M(a(u)) Δu + F(u) + γ u’ = fwhere F is a Lipschitz function.

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