The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain

Masaru Ikehata

doi:10.3934/ipi.2016.10.131

Article Contents

2016, Volume 10, Issue 1: 131-163. Doi: 10.3934/ipi.2016.10.131 open access

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The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain

Masaru Ikehata^1,

1.
Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi Hiroshima 739-8527

Received: September 30, 2014

Revised: June 30, 2015

Published: January 2016

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Abstract

In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an orientation and supported outside an unknown obstacle and observed on the same support over a finite time interval. It is assumed that the obstacle is a perfect conductor. Two types of analytical formulae which employ a single observed wave and explicitly contain information about the geometry of the obstacle are given. In particular, an effect of the orientation of the current is catched in one of two formulae. Two corollaries concerning with the detection of the points on the surface of the obstacle nearest to the centre of the current support and curvatures at the points are also given.

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Mathematics Subject Classification: Primary: 35R30, 35L50, 35Q61; Secondary: 78A46, 78M35.

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