scholarly journals Local energy decay and Strichartz estimates for the wave equation with time-periodic perturbations

2006 ◽  
pp. 267-285 ◽  
Author(s):  
Vesselin Petkov
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Strichartz Estimates ◽  
Local Energy ◽  
Periodic Perturbations ◽  
Time Periodic

scholarly journals Local energy decay for the damped wave equation

2014 ◽  
Vol 266 (7) ◽  
pp. 4538-4615 ◽  
Author(s):  
Jean-Marc Bouclet ◽  
Julien Royer
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Local Energy ◽  
Damped Wave Equation

scholarly journals Local Energy Decay for the Wave Equation

2016 ◽  
Vol 63 (10) ◽  
pp. 1158-1159
Author(s):  
Jason Metcalfe
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Local Energy

scholarly journals Improved local energy decay for the wave equation on asymptotically Euclidean odd dimensional manifolds in the short range case

2012 ◽  
Vol 12 (3) ◽  
pp. 635-650 ◽  
Author(s):  
Jean-François Bony ◽  
Dietrich Häfner
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Short Range ◽  
Energy Decay ◽  
Weighted Spaces ◽  
Local Energy ◽  
Euclidean Metric ◽  
Odd Dimensions

AbstractWe show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give estimates of powers of the resolvent of the wave propagator between weighted spaces.

scholarly journals Local energy decay for the wave equation with a nonlinear time-dependent damping

2013 ◽  
Vol 92 (11) ◽  
pp. 2288-2308 ◽  
Author(s):  
Ahmed Bchatnia ◽  
Moez Daoulatli
Keyword(s):  
Wave Equation ◽  
Energy Decay ◽  
Time Dependent ◽  
Local Energy

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

High Frequency Resolvent Estimates and Energy Decay of Solutions to the Wave Equation

2004 ◽  
Vol 47 (4) ◽  
pp. 504-514 ◽  
Author(s):  
Fernando Cardoso ◽  
Georgi Vodev
Keyword(s):  
Wave Equation ◽  
Real Axis ◽  
Riemannian Manifolds ◽  
High Frequency ◽  
Beltrami Operator ◽  
Energy Decay ◽  
Local Energy ◽  
Resolvent Estimates ◽  
The Real ◽  
Decay Of Solutions

AbstractWe prove an uniform Hölder continuity of the resolvent of the Laplace-Beltrami operator on the real axis for a class of asymptotically Euclidean Riemannian manifolds. As an application we extend a result of Burq on the behaviour of the local energy of solutions to the wave equation.

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