Article Contents

2015, Volume 9, Issue 4: 951-970. Doi: 10.3934/ipi.2015.9.951

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The inverse electromagnetic scattering problem by a mixed impedance screen in chiral media

1.
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, 157 84 Athens
2.
Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou Str., 185 34 Piraeus

Received: December 2014

Revised: July 2015

Published: November 2015

Abstract / Introduction Related Papers Cited by

Abstract

In this paper the problem of scattering of time-harmonic electromagnetic waves by a mixed impedance scatterer in chiral media is considered. Our scatterer is a partially coated chiral screen, for which an impedance boundary condition on one side of its boundary, and a perfectly conducting boundary condition on the other side, is satisfied. The direct scattering problem for the modified Maxwell equations is formulated and the appropriate Sobolev space setting is considered. Issues of solvability due to uniqueness and existence are discussed. The corresponding inverse scattering problem is studied and uniqueness results concerning the mixed impedance screen are proved. Further, the shape reconstruction of the boundary of the partially coated screen is established. In particular, a chiral far-field operator is introduced and new results concerning its properties are proved. A modified linear sampling method based on a factorization of the chiral far-field operator, in order to reconstruct the screen is also presented. We end up with useful conclusions and remarks for screens in chiral media.

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Mathematics Subject Classification: Primary: 35Q60, 78A46; Secondary: 46E35, 45Q05.

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