On finding the surface admittance of an obstacle via the time domain enclosure method

Masaru Ikehata

doi:10.3934/ipi.2019014

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2019, Volume 13, Issue 2: 263-284. Doi: 10.3934/ipi.2019014 open access

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On finding the surface admittance of an obstacle via the time domain enclosure method

Masaru Ikehata

Laboratory of Mathematics, Graduate School of Engineering, Hiroshima University, Higashihiroshima 739-8527, Japan

Received: May 31, 2017

Revised: July 31, 2018

Published: March 2019

The author was partially supported by Grant-in-Aid for Scientific Research (C)(No 17K05331) of Japan Society for the Promotion of Science.

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Abstract

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an unknown obstacle. The condition is described by using an unknown positive function on the surface of the obstacle which is called the surface admittance. The wave is generated at the initial time by a volumetric current source supported on a very small ball placed outside the obstacle and only the electric component of the wave is observed on the same ball over a finite time interval. It is shown that from the observed data one can extract information about the value of the surface admittance and the curvatures at the points on the surface nearest to the center of the ball. This shows that a single shot contains a meaningful information about the quantitative state of the surface of the obstacle.

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

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