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arXiv 1709.020022017-09-06math.AP

Recovery of non compactly supported coefficients of elliptic equations on an infinite waveguide

Yavar Kian

英文摘要：

We consider the unique recovery of a non compactly supported and non periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different context including recovery of some general class of coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.

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本文研究了从稀疏边界测量中恢复热方程中点源的逆问题，利用分析工具和数值实验证明了点源位置和幅值的唯一恢复。

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