Local energy decay for the nonlinear dissipative wave equation in an exterior domain

2007 ◽  
pp. 39-65 ◽  
Author(s):  
Moez Daoulatli
Keyword(s):  
Wave Equation ◽  
Exterior Domain ◽  
Energy Decay ◽  
Local Energy ◽  
Dissipative Wave Equation

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

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

ON LOCAL ENERGY DECAY ESTIMATE OF THE OSEEN SEMIGROUP IN TWO DIMENSIONS AND ITS APPLICATION

2019 ◽  
pp. 1-33 ◽  
Author(s):  
Yasunori Maekawa
Keyword(s):  
Exterior Domain ◽  
Decay Estimate ◽  
Two Dimensions ◽  
Energy Decay ◽  
Local Energy ◽  
Two Dimensional ◽  
Translation Speed ◽  
Temporal Decay ◽  
Oseen Semigroup

We study the temporal decay estimate of the Oseen semigroup in a two-dimensional exterior domain. We establish the local energy decay estimate with a suitable dependence on the small translation speed, which is a significant improvement of Hishida’s result in 2016. As an application, we prove the $L^{q}$ - $L^{r}$ estimates of the Oseen semigroup uniformly in the small translation speed.

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.

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