论文标题
在浅管中，有周期性水池家族的水波问题频谱的带隙结构
Band-gap structure of the spectrum of the water-wave problem in a shallow canal with a periodic family of deep pools
论文作者
论文摘要
我们考虑了周期性通道中的线性水波问题$π^h \ subset \ mathbb {r}^3 $，除了周期性的深坑洼阵列外，它是浅的。通过应用于表面波传播现象的应用，我们研究了线性水波系统中必需光谱的带隙结构，其中包括在游离水面上构成的光谱steklov边界条件。我们采用渐近分析的方法，其中最涉及的步骤是与通道薄部分的坑洼关节邻域中适当的边界层的构建和分析。因此，证明了足够小$ h $的光谱差距的存在。
We consider the linear water-wave problem in a periodic channel $Π^h \subset \mathbb{R}^3$, which is shallow except for a periodic array of deep potholes in it. Motivated by applications to surface wave propagation phenomena, we study the band-gap structure of the essential spectrum in the linear water-wave system, which includes the spectral Steklov boundary condition posed on the free water surface. We apply methods of asymptotic analysis, where the most involved step is the construction and analysis of an appropriate boundary layer in a neighborhood of the joint of the potholes with the thin part of the channel. Consequently, the existence of a spectral gap for small enough $h$ is proven.
