Consider the direct and inverse scattering problem of time harmonic acoustic waves by a two-dimensional elastic obstacle which contains an unknown impenetrable object inside. We apply the boundary integral equation method to solve the direct scattering problem. Since the obtained boundary integral system is a mixed form of scalar and vector equations, we consider the existence of the solution in the sense of a weak formulation. The factorization method is employed to solve the corresponding inverse scattering problem, that is, we try to recover the shape of the interaction surface from the knowledge of acoustic far-field patterns. With the help of a special data to pattern operator G , we can reconstruct the shape of the interaction surface by using the classical factorization method. Furthermore, a new mixed reciprocity relation is proposed to show the relation between the interior elastic field and unitary matrix 𝒮{\mathcal{S}}.

中文翻译：

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未知掩埋物体的流固相互作用散射问题

考虑由二维弹性障碍物引起的时间谐波声波的正向和反向散射问题，该障碍物内部包含未知的不可穿透的物体。我们应用边界积分方程法来解决直接散射问题。由于获得的边界积分系统是标量方程和矢量方程的混合形式，因此从弱公式的意义上考虑解决方案的存在。分解法被用来解决相应的逆散射问题，也就是说，我们试图从声学远场模式的知识中恢复相互作用表面的形状。借助于模式算子G的特殊数据，我们可以使用经典的因式分解方法来重建交互表面的形状。此外，