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arXiv · 1605.06599

An inverse problem for the magnetic Schrödinger equation in infinite cylindrical domains

Mourad Bellassoued·Yavar Kian·Eric Soccorsi
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Abstract

We study the inverse problem of determining the magnetic field and the electric potential entering the Schrödinger equation in an infinite 3D cylindrical domain, by Dirichlet-to-Neumann map. The cylindrical domain we consider is a closed waveguide in the sense that the cross section is a bounded domain of the plane. We prove that the knowledge of the Dirichlet-to-Neumann map determines uniquely, and even Hölder-stably, the magnetic field induced by the magnetic potential and the electric potential. Moreover, if the maximal strength of both the magnetic field and the electric potential, is attained in a fixed bounded subset of the domain, we extend the above results by taking finitely extended boundary observations of the solution, only.

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Mourad Bellassoued, Yavar Kian, Eric Soccorsi. 2016-05-21. An inverse problem for the magnetic Schrödinger equation in infinite cylindrical domains. https://arxiv.org/abs/1605.06599

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