scholarly journals Local Energy Decay for Linear Wave Equations with Localized Dissipation

2005 ◽  
Vol 48 (3) ◽  
pp. 351-366 ◽  
Author(s):  
Ryo Ikehata
Keyword(s):  
Wave Equations ◽  
Energy Decay ◽  
Linear Wave ◽  
Local Energy ◽  
Linear Wave Equations

scholarly journals Scattering for critical wave equations with variable coefficients

2021 ◽  
pp. 1-19
Author(s):  
Shi-Zhuo Looi ◽  
Mihai Tohaneanu
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Variable Coefficients ◽  
Energy Decay ◽  
Time Dependent ◽  
Linear Wave ◽  
Decay Estimates ◽  
Local Energy ◽  
Linear Wave Equation ◽  
Semilinear Wave Equation

Abstract We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$ scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$ , but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$ norm of the solution as $t\to \infty$ .

Uniqueness for stochastic non-linear wave equations

2007 ◽  
Vol 67 (12) ◽  
pp. 3287-3310 ◽  
Author(s):  
Martin Ondreját
Keyword(s):  
Wave Equations ◽  
Linear Wave ◽  
Non Linear ◽  
Linear Wave Equations
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