The enclosure method for the anisotropic maxwell system

Rulin Kuan, Yi-Hsuan Lin, Mourad Sini

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable and impenetrable obstacles in an 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 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- Lp estimate, for the Maxwell system, to compare the integrals coming from oscillating-decaying solutions and those from the reflected solutions.

Original languageEnglish
Pages (from-to)3488-3527
Number of pages40
JournalSIAM Journal on Mathematical Analysis
Volume47
Issue number5
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Enclosure method
  • Meyers L estimates
  • Oscillating-decaying solutions
  • Reconstruction
  • Runge approximation property

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