Energy decay of the wave equation with variable coefficients and a localized half-linear dissipation in an exterior domain

2013 ◽  
Vol 66 (1) ◽  
pp. 95-112 ◽  
Author(s):  
Jing Li ◽  
Shugen Chai ◽  
Jieqiong Wu
Keyword(s):  
Wave Equation ◽  
Exterior Domain ◽  
Variable Coefficients ◽  
Energy Decay

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 $t\to \infty$ .

Lp-estimates for the wave equation with time-dependent dissipation

2005 ◽  
Vol 135 (2) ◽  
pp. 393-412
Author(s):  
Tokio Matsuyama
Keyword(s):  
Wave Equation ◽  
Exterior Domain ◽  
Wave Speed ◽  
Energy Decay ◽  
Time Dependent ◽  
Local Energy ◽  
Lp Estimates ◽  
Dissipative Wave Equation ◽  
Scattering Rates

We are interested in Lp-estimates and scattering rates for the dissipative wave equation with time-dependent coefficients in an exterior domain outside a star-shaped obstacle. We want to notice the case that the support of dissipation expands strictly less than the wave speed. We develop a new cut-off method, which is time dependent. For this, we shall obtain the local energy decay over the time-dependent subdomain

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