Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Yi-Hsuan Lin*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We develop an enclosure-type reconstruction scheme to identify penetrable obstacles in acoustic waves with anisotropic medium in ℝ3. The main difficulty of treating this problem lies in the fact that there are no complex geometrical optics solutions available for the acoustic equation with anisotropic medium in ℝ3. Instead, we will use another type of special solutions called oscillating-decaying solutions. Even though that oscillating-decaying solutions are defined only on the half space, we are able to give necessary boundary inputs by the Runge approximation property. Moreover, since we are considering a Helmholtz-type equation, we turn to Meyers' Lp estimate to compare the integrals coming from oscillating-decaying solutions and those from reected solutions.

Original languageEnglish
Pages (from-to)765-780
Number of pages16
JournalInverse Problems and Imaging
Volume10
Issue number3
DOIs
StatePublished - 1 Aug 2016

Keywords

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

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