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

  • Masaru Ikehata ORCID logo EMAIL logo
Veröffentlicht/Copyright: 31. März 2023

Abstract

The time domain enclosure method is one of the 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.

Award Identifier / Grant number: 17K05331

Award Identifier / Grant number: 18H01126

Funding statement: The author was partially supported by Grant-in-Aid for Scientific Research (C)(No. 17K05331) and (B)(No. 18H01126) of Japan Society for the Promotion of Science.

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Received: 2020-11-24
Revised: 2020-12-23
Accepted: 2023-01-30
Published Online: 2023-03-31
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 29.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jiip-2020-0150/html
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