Reconstruction of a potential from the impedance boundary map

M. I. Isaev, R. G. Novikov

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We consider the inverse boundary value problem for the Schrödinger equation at fixed energy with boundary measurements represented as the impedance boundary map (or Robin-to-Robin map). We give formulas and equations for finding (generalized) scattering data for the aforementioned equation from boundary measurements in this impedance representation. Combining these results with results of the inverse scattering theory we obtain efficient methods for reconstructing potential from the impedance boundary map. To our knowledge, results of the present work are new already for the case of Neumann-to-Dirichlet map.

Original languageEnglish
Pages (from-to)5-28
Number of pages24
JournalEurasian Journal of Mathematical and Computer Applications
Volume1
Issue number1
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Generalized scattering data
  • Inverse boundary value problems
  • Reconstruction methods
  • Robin-to-Robin map

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