论文标题
kelvin-voigt阻尼波方程的衰减：分段光滑阻尼
Decay for the Kelvin-Voigt damped wave equation: Piecewise smooth damping
论文作者
论文摘要
我们研究了开尔文 - 伏伊氏阻尼波方程的能量衰减速率，并在多维结构域上进行分段平滑阻尼。在对阻尼支持的合适几何假设下，我们获得了最佳多项式衰变率，事实证明，它与\ cite {lr05}中研究的一维情况不同。这种最佳衰减速率被定位在几何光学射线上的高能准模型饱和，这些射线沿着非正交的界面都击中了界面。证明使用边界价值问题的半古典分析。
We study the energy decay rate of the Kelvin-Voigt damped wave equation with piecewise smooth damping on the multi-dimensional domain. Under suitable geometric assumptions on the support of the damping, we obtain the optimal polynomial decay rate which turns out to be different from the one-dimensional case studied in \cite{LR05}. This optimal decay rate is saturated by high energy quasi-modes localised on geometric optics rays which hit the interface along non orthogonal neither tangential directions. The proof uses semi-classical analysis of boundary value problems.
