Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering amplitude. The first one is a local uniqueness in determining a variable index of refraction by the fixed incident-direction scattering amplitude. The inverse problem is formally posed with such measurement data. The second one is a global uniqueness in determining a constant refractive index by a single far-field measurement. The arguments are based on the study of certain non-self-adjoint interior transmission eigenvalue problems.

Keywords

formally-determined, interior transmission eigenvalues, inverse scattering, refractive index, uniqueness

Publication Date

6-2015

Source Publication Title

Applicable Analysis

Volume

94

Issue

6

Start Page

1259

End Page

1269

Publisher

Taylor & Francis

Peer Reviewed

1

Copyright

This is an Accepted Manuscript of an article published by Taylor & Francis in Applicable Analysis in June 2015, available online: http://www.tandfonline.com/10.1080/00036811.2014.924215.

Funder

This work was supported by the German Research Foundation (DFG), [grant number HU 2111/1-1]; the NSF of China [grant number 11371115], [grant number 11201453], [grant number 91130022] and the NSF grant, DMS 1207784.

DOI

10.1080/00036811.2014.924215

ISSN (print)

00036811

ISSN (electronic)

1563504X

Included in

Mathematics Commons

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