Reconstruction of penetrable inclusions in elastic waves by boundary measurements

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2 Citations (Scopus)

Abstract

We use Ikehata's enclosure method to reconstruct penetrable unknown inclusions in a plane elastic body in time-harmonic waves. Complex geometrical optics solutions with complex polynomial phases are adopted as the probing utility. In a situation similar to ours, due to the presence of a zeroth order term in the equation, some technical assumptions need to be assumed in early researches. In a recent work of Sini and Yoshida, they succeeded in abandoning these assumptions by using a different idea to obtain a crucial estimate. In particular the boundaries of the inclusions need only to be Lipschitz. In this work we apply the same idea to our model. It's interesting that, with more careful treatment, we find the boundaries of the inclusions can in fact be assumed to be only continuous.

Original languageEnglish
Pages (from-to)1494-1520
Number of pages27
JournalJournal of Differential Equations
Volume252
Issue number2
DOIs
Publication statusPublished - 2012 Jan 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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