Inverse Problems for Obstacles in a Waveguide

In this paper we prove that a particular entry in the scattering matrix, if known for all energies, determines certain rotationally symmetric obstacles in a generalized waveguide. The generalized waveguide X can be of any dimension and we allow either Dirichlet or Neumann boundary conditions on the...

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Bibliographic Details
Published in:Communications in partial differential equations 2010-02, Vol.35 (2), p.328-352
Main Authors: Christiansen, T. J., Taylor, Michael
Format: Article
Language:English
Subjects:
Cylindrical ends
Inverse problems
Partial differential equations
Scattering matrix
Studies
Waveguide
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Summary:In this paper we prove that a particular entry in the scattering matrix, if known for all energies, determines certain rotationally symmetric obstacles in a generalized waveguide. The generalized waveguide X can be of any dimension and we allow either Dirichlet or Neumann boundary conditions on the boundary of the obstacle and on ∂X. In the case of a two-dimensional waveguide, two particular entries of the scattering matrix suffice to determine the obstacle, without the requirement of symmetry.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605300903296298