关于根据部分边界测量确定麦克斯韦方程中电磁参数的逆问题

Christian Daveau, Islem Ben Hnia, Abdessatar Khelifi
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引用次数: 0

摘要

在本文中,我们处理了麦克斯韦方程的反边界值问题,假定边界数据仅在边界的可访问部分 \(\Gamma \)是已知的。我们的目的是利用仅限于边界开放部分的测量值的狄利克特到诺依曼数据来证明唯一性结果,并试图重建物体内部的复折射率 \({{\varvec{n}}}\)。此外,利用局限于 \(\Gamma \)的阻抗图,我们可以确定折射率小体积分数扰动的位置。
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On an inverse problem of determining electromagnetic parameters in Maxwell’s equations from partial boundary measurements

In this paper, we deal with an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part \(\Gamma \) of the boundary. We aim to prove uniqueness results using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index \({{\varvec{n}}}\) in the interior of a body. Further, using the impedance map restricted to \(\Gamma \), we may identify locations of small volume fraction perturbations of the refractive index.

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