Local energy decay for the damped Klein-Gordon equation in exterior domain

2016 ◽  
Vol 96 (2) ◽  
pp. 349-362 ◽  
Author(s):  
Mohamed Malloug
Keyword(s):  
Exterior Domain ◽  
Gordon Equation ◽  
Energy Decay ◽  
Local Energy ◽  
Klein Gordon ◽  
Klein Gordon Equation

Time decay for the nonlinear Klein-Gordon equation

1968 ◽  
Vol 306 (1486) ◽  
pp. 291-296 ◽  
Keyword(s):  
Gordon Equation ◽  
Initial Energy ◽  
Local Energy ◽  
Time Decay ◽  
Systems Of Equations ◽  
Second Derivatives ◽  
Klein Gordon ◽  
Piecewise Continuous ◽  
Klein Gordon Equation

It is shown that solutions of the nonlinear Klein-Gordon equation u tt - ∆ u + mu + P '( u ) = 0 decay to zero in the local L 2 mean if the initial energy is bounded provided s P ') s ) - 2 P ( s ) ≥ a P ( s ) ≥ 0 with a > 0. The local energy also decays. The proof is based on manipulating energy identities and re­quires that u have continuouś first derivatives and piecewise continuous second derivatives. The proof is also applicable to certain systems of equations.

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