We study how to apply the enclosure method to reconstruct an unknown inclusion within a medium in a domain in which satisfies the conductivity equation ∇ ⋅ ((σ ₀ + iɛ ₀)∇u) = 0 with σ ₀ and ɛ ₀ being real matrix functions. Motivated by some real world applications, we assume the unknown inclusion satisfies an equation of the more general form , where σ, ɛ, ζ are also real matrix functions. Due to the anisotropy, it is in general difficult to find complex geometric optics solutions. Therefore, we construct the oscillating decaying solutions, which is used to test whether a given half-space intersects the unknown inclusion or not.

中文翻译：

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广义各向异性复电导率方程的封闭法

我们研究如何应用封闭法在满足电导方程 ∇ ⋅ (( σ ₀ + i ɛ ₀ )∇ u ) = 0 且σ ₀和ɛ ₀为实矩阵的域中重构介质中的未知夹杂物功能。受一些现实世界应用的启发，我们假设未知包含满足更一般形式的方程，其中σ , ɛ , ζ也是实矩阵函数。由于各向异性，通常很难找到复杂的几何光学解决方案。因此，我们构造了振荡衰减解，用于测试给定的半空间是否与未知包含物相交。