沿边界穿孔墙的吸声
Sound absorption by perforated walls along boundaries
摘要：
我们分析了复域上的Helmholtz方程。通过具有周期性$\varepsilon>0$的周期性几何形状来对边界的一部分处的吸声结构进行建模。厚度为$\varepsilon$的谐振器体积通过薄通道（开口$\varepsilon^3$）与宏观域的主要部分连接。对于这三种不同尺度的问题，我们分析了极限$\varepsilon\to 0$下的解，发现有效系统可以描述声吸收。
英文摘要：
We analyze the Helmholtz equation in a complex domain. A sound absorbing structure at a part of the boundary is modelled by a periodic geometry with periodicity $\varepsilon>0$. A resonator volume of thickness $\varepsilon$ is connected with thin channels (opening $\varepsilon^3$) with the main part of the macroscopic domain. For this problem with three different scales we analyze solutions in the limit $\varepsilon\to 0$ and find that the effective system can describe sound absorption.
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