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A Mixed Impedance Scattering Problem for Partially Coated Obstacles in Two-Dimensional Linear Elasticity

In: Integral Methods in Science and Engineering

Author

Listed:
  • C. E. Athanasiadis

    (National and Kapodistrian University of Athens)

  • D. Natroshvili

    (Georgian Technical University)

  • V. Sevroglou

    (University of Piraeus)

  • I. G. Stratis

    (National and Kapodistrian University of Athens)

Abstract

In this paper the problem of scattering of time-harmonic elastic waves by a non-penetrable partially coated obstacle buried in a piecewise homogeneous medium is considered. We study the direct scattering problem as well as the inverse one. The direct problem for the Navier equation is formulated in a dyadic form and the issues of solvability due to uniqueness, existence and regularity are discussed. Uniqueness results for the corresponding inverse scattering problem are proved. In particular, the unique determination of the non-penetrable partially coated obstacle with its boundary condition as well as of the penetrable interface(s) between the layered media are established via the knowledge of the far-field pattern for elastic waves. The proof of the uniqueness is based on a mixed reciprocity relation and its connection between plane-waves and point-sources. The paper at hand deals with two-dimensional problems for a body consisting of two layers, but the obtained results also hold for multi-layered media; they are valid as well for the three-dimensional case.

Suggested Citation

  • C. E. Athanasiadis & D. Natroshvili & V. Sevroglou & I. G. Stratis, 2015. "A Mixed Impedance Scattering Problem for Partially Coated Obstacles in Two-Dimensional Linear Elasticity," Springer Books, in: Christian Constanda & Andreas Kirsch (ed.), Integral Methods in Science and Engineering, edition 1, chapter 0, pages 29-41, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16727-5_3
    DOI: 10.1007/978-3-319-16727-5_3
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