Decoupling elastic waves and its applications

Hongyu LIU*, Jingni Xiao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

In this paper, we consider time-harmonic elastic wave scattering governed by the Lamé system. It is known that the elastic wave field can be decomposed into the shear and compressional parts, namely, the pressure and shear waves that are generally coexisting, but propagating at different speeds. We consider the third or fourth kind impenetrable scatterer and derive two geometric conditions, respectively, related to the mean and Gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves. The decoupling results are new to the literature and are of significant interest for their own sake. As an interesting application, we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far-field measurements.

Original languageEnglish
Pages (from-to)4442-4480
Number of pages39
JournalJournal of Differential Equations
Volume263
Issue number8
DOIs
Publication statusPublished - 15 Oct 2017

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Decoupling
  • Elastic scattering
  • Inverse elastic scattering
  • Lamé system
  • Shear and pressure waves
  • Uniqueness and stability

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