论文标题
具有应用的声学弹性传输特征值问题的光谱特性
Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications
论文作者
论文摘要
我们关注的是在声学和弹性波的耦合传播中引起的耦合 - 物理光谱问题，这被称为声学弹性传递特征值问题。这项工作中有两个主要贡献是文献的新作用。首先，在中等参数的温和条件下，我们证明存在声弹性传输特征值。其次，我们通过表明它们倾向于定位在基础域的边界上，从而建立了透射本征函数的几何刚度结果。此外，我们还考虑了通过使用起泡的弹性结构以及与流体结构相互作用相关的逆问题，获得了获得的结果对超材料的有效构建的有趣含义。
We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in this work which are new to the literature. First, under a mild condition on the medium parameters, we prove the existence of an acoustic-elastic transmission eigenvalue. Second, we establish a geometric rigidity result of the transmission eigenfunctions by showing that they tend to localize on the boundary of the underlying domain. Moreover, we also consider interesting implications of the obtained results to the effective construction of metamaterials by using bubbly elastic structures and to the inverse problem associated with the fluid-structure interaction.
