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

2017/09/06 by Yavar Kian, Kian, Yavar · 1 citation
Mathematics · Computer Science · Engineering · #Numerical methods in inverse problems #Advanced Mathematical Modeling in Engineering #Microwave Imaging and Scattering Analysis

paper · pdf · doi:10.48550/arxiv.1709.02002

Abstract

We consider the unique recovery of a non compactly supported and non periodic\nperturbation of a Schr "odinger operator in an unbounded cylindrical domain,\nalso called waveguide, from boundary measurements. More precisely, we prove\nrecovery of general class of electric potentials from the partial\nDirichlet-to-Neumann map, where the Dirichlet data is supported on slightly\nmore than half of the boundary and the Neumann data is taken on the other half\nof the boundary. We apply this result in different context including recovery\nof some general class of coefficients from measurements on a bounded subset and\nrecovery of an electric potential, supported on an unbounded cylinder, of a\nSchr "odinger operator in a slab.\n

Citations

• Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map
• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

Cited by

• Stable recovery of a non-compactly supported coefficient of a\n Schr "odinger equation on an infinite waveguide

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