Can a single scalar second order PDE govern well the propagation of the electric wave field in a heterogeneous 3D medium?-Reference-Cited by-同舟云学术

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

Published:2022-04-28 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Romanov Vladimir G.¹,Klibanov Michael V.²

Affiliation:

1. Sobolev Institute of Mathematics , 630090; and Mathematical Center in Akademgorodok, Novosibirsk State University , Novosibirsk , Russia

2. Department of Mathematics and Statistics , University of North Carolina at Charlotte , Charlotte , NC 28223 , USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2021-0085/pdf

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