Electromagnetic wave scattering by an elastic body in a two-layered medium

This paper is concerned with the electromagnetic scattering by an elastic body embedded in a two-layered medium, which is modeled by Maxwell’s and Navier equations with a coupled interaction condition. A uniqueness result is first obtained by imposing the Silver–Müller radiation condition in each layer. Then the existence of a solution is shown by proposing three coupling methods combining integral equations (or integral representation) and variational formulas. Based on the well-posedness of the interaction model, a uniqueness theorem is proved for the inverse problem of determining the elastic body in a two-layered medium by partial electromagnetic field measurements in the upper-half space.

Keywords

Maxwell’s equations, Navier equation, two-layered medium, well-posedness, inverse problem, uniqueness

2010 Mathematics Subject Classification

35P25, 35Q60, 35R30, 74F15

Full Text (PDF format)

Received 4 August 2021

Received revised 1 September 2023

Accepted 7 October 2023

Published 12 July 2024