We consider the problem of interior scattering from a point source for a bounded domain D containing two penetrable scatterers \(\Omega _1\) and \(\Omega _2\) in \(R^2\). The integral representation for a solution is reconstructed in the form of special combined potentials. The density functions included in the potentials satisfy the uniquely solvable Riesz-Fredholm integral equation. Then we obtain the existence and uniqueness of the solution for the direct scattering problem.

中文翻译：

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空腔中可穿透障碍物的直接散射问题

我们考虑从一个点源的内部散射问题，一个有界域D包含两个可穿透的散射体\(\Omega _1\)和\(\Omega _2\) in \(R^2\)。解决方案的积分表示以特殊组合势的形式重建。包含在势能中的密度函数满足唯一可解的 Riesz-Fredholm 积分方程。然后我们得到直接散射问题解的存在唯一性。