On an inverse problem of determining electromagnetic parameters in Maxwell’s equations from partial boundary measurements

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 75; no. 5
• Main Authors: Daveau, Christian, Ben Hnia, Islem, Khelifi, Abdessatar
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2024; Springer Nature B.V; Springer Verlag
• Subjects: Boundary value problems; Engineering; Inverse problems; Mathematical Methods in Physics; Mathematics; Maxwell's equations; Parameter identification; Refractivity; Theoretical and Applied Mechanics; Reconstruction; Electromagnetic parameters; 35R30; Maxwell equations; 35Q61; Partial data; Inverse problem; 78M35; partial data; reconstruction Mathematics Subject Classifications: (MSC2010) 35Q61; Inverse problem Maxwell equations electromagnetic coefficients partial data reconstruction Mathematics Subject Classifications: (MSC2010) 35Q61 78M35 35R30; electromagnetic coefficients
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-024-02299-4

In this paper, we deal with an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part Γ of the boundary. We aim to prove uniqueness results using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index n in the interior of a body. Further, using the impedance map restricted to Γ , we may identify locations of small volume fraction perturbations of the refractive index.