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Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium? / Romanov, Vladimir G.; Klibanov, Michael V.

In: Journal of Inverse and Ill-Posed Problems, Vol. 30, No. 4, 01.08.2022, p. 595-611.

Research output: Contribution to journal › Article › peer-review

Harvard

Romanov, VG & Klibanov, MV 2022, 'Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?', Journal of Inverse and Ill-Posed Problems, vol. 30, no. 4, pp. 595-611. https://doi.org/10.1515/jiip-2021-0085

APA

Romanov, V. G., & Klibanov, M. V. (2022). Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium? Journal of Inverse and Ill-Posed Problems, 30(4), 595-611. https://doi.org/10.1515/jiip-2021-0085

Vancouver

Romanov VG, Klibanov MV. Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium? Journal of Inverse and Ill-Posed Problems. 2022 Aug 1;30(4):595-611. doi: 10.1515/jiip-2021-0085

Author

Romanov, Vladimir G. ; Klibanov, Michael V. / Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?. In: Journal of Inverse and Ill-Posed Problems. 2022 ; Vol. 30, No. 4. pp. 595-611.

BibTeX

@article{ff38374965db4563ace2739bbea99f7d,
title = "Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?",
abstract = "It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single scalar second order PDE, which is derived from Maxwell's equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single scalar second order PDE rather than with the complete Maxwell system, the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media. ",
keywords = "domination of one component, experimental data for inverse problems, geodesic lines, Maxwell's equations",
author = "Romanov, {Vladimir G.} and Klibanov, {Michael V.}",
note = "Publisher Copyright: {\textcopyright} 2022 Walter de Gruyter GmbH, Berlin/Boston.",
year = "2022",
month = aug,
day = "1",
doi = "10.1515/jiip-2021-0085",
language = "English",
volume = "30",
pages = "595--611",
journal = "Journal of Inverse and Ill-Posed Problems",
issn = "0928-0219",
publisher = "Walter de Gruyter GmbH",
number = "4",

}

RIS

TY - JOUR

T1 - Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?

AU - Romanov, Vladimir G.

AU - Klibanov, Michael V.

N1 - Publisher Copyright: © 2022 Walter de Gruyter GmbH, Berlin/Boston.

PY - 2022/8/1

Y1 - 2022/8/1

N2 - It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single scalar second order PDE, which is derived from Maxwell's equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single scalar second order PDE rather than with the complete Maxwell system, the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.

AB - It is demonstrated in this paper that the propagation of the electric wave field in a heterogeneous medium in 3D can sometimes be governed well by a single scalar second order PDE, which is derived from Maxwell's equations. The corresponding component of the electric field dominates two other components. This justifies some past results of the second author with coauthors about numerical solutions of coefficient inverse problems with experimental electromagnetic data. In addition, since it is simpler to work in applications with a single scalar second order PDE rather than with the complete Maxwell system, the result of this paper might be useful to researchers working on applied issues of the propagation of electromagnetic waves in inhomogeneous media.

KW - domination of one component

KW - experimental data for inverse problems

KW - geodesic lines

KW - Maxwell's equations

UR - http://www.scopus.com/inward/record.url?scp=85127807174&partnerID=8YFLogxK

U2 - 10.1515/jiip-2021-0085

DO - 10.1515/jiip-2021-0085

M3 - Article

AN - SCOPUS:85127807174

VL - 30

SP - 595

EP - 611

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

SN - 0928-0219

IS - 4

ER -

ID: 36864488