The enclosure method for the anisotropic Maxwell system

2015/01/07 by Rulin Kuan, Yi‐Hsuan Lin, Kuan, Rulin +3 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1501.01533

openalex publication_date 2015/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable and impenetrable obstacles in electromagnetic field with anisotropic medium in ℝ³. The main difficulty in treating this problem lies in the fact that there are so far no complex geometrical optics solutions available for the Maxwell's equation with anisotropic medium in ℝ³. Instead, we derive and use another type of special solutions called oscillating-decaying solutions. To justify this scheme, we use Meyers' L^p estimate, for the Maxwell system, to compare the integrals coming from oscillating-decaying solutions and those from the reflected solutions.

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