On finding a penetrable obstacle using a single electromagnetic wave in the time domain

Abstract

The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell system and consists of two parts. The first part establishes the base of the time domain enclosure method for the Maxwell system using a single set of the solutions over a finite time interval for a general (isotropic) inhomogeneous medium in the whole space. It is a system of asymptotic inequalities for the indicator function which may enable us to apply the time domain enclosure method to the problem of finding unknown penetrable obstacles embedded in various background media. As a first step of its expected applications, the case when the background medium is homogeneous and isotropic, is considered and the time domain enclosure method is realized. This is the second part.

22 pages, self revision, introduction revised, on page 5 conditions (B.I), (B.II) and (B.III) introduced, Theorem 1.2 revised, on page 6 another indicator function introduced, Corollary 1.1 created, subsection 3.3 revised, Lemma 3.2 together with the proof revised, grant information added, references [2], [25] added

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