The Fixed Point Iteration and Newton’s Methods for the Nonlinear Wave Equation

2008 ◽  
Author(s):  
Igor V. Shevchenko
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Fixed Point Iteration ◽  
Newton's Methods

scholarly journals On a nonolinear wave equation in unbounded domains

1988 ◽  
Vol 11 (2) ◽  
pp. 335-342 ◽  
Author(s):  
Carlos Frederico Vasconcellos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Wave Phenomenon ◽  
Energy Method ◽  
Unbounded Domains ◽  
Homogeneous Media

We study existence and uniqeness of the nonlinear wave equation∂2u∂t2+M(x,∫|∇u(x,t)|2dx+∫|u(x,t)|2dx)(−Δu+u)=0in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.

On the global existence and asymptotic behavior of the solution of a nonlinear wave equation with past history

2021 ◽  
Vol 62 (3) ◽  
pp. 031512
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Mohammad Kafini ◽  
Shadi Al-Omari
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Past History
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