The factorization method for a partially coated cavity in inverse scattering

Qinghua  Wu; Guozheng  Yan

doi:10.3934/ipi.2016.10.263

Article Contents

2016, Volume 10, Issue 1: 263-279. Doi: 10.3934/ipi.2016.10.263

This issue Previous Article A partial data result for less regular conductivities in admissible geometries Next Article

The factorization method for a partially coated cavity in inverse scattering

Qinghua Wu^1, and
Guozheng Yan^1,

1.
School of Mathematics and Statistics, Central China Normal University, Wuhan

Received: December 31, 2014

Revised: June 30, 2015

Published: January 2016

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Abstract

We consider the interior inverse scattering problem of recovering the shape of an impenetrable partially coated cavity. The scattered fields incited by point source waves are measured on a closed curve inside the cavity. We prove the validity of the factorization method for reconstructing the shape of the cavity. However, we are not able to apply the basic theorem introduced by Kirsch and Grinberg to treat the key operator directly, and some auxiliary operators have to be considered. In this paper, we provide theoretical validation of the factorization method to the problem, and some numerical results are presented to show the viability of our method.

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Mathematics Subject Classification: Primary: 35C15, 35Q65; Secondary: 78A45.

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