Elastic scattering problems by penetrable obstacles with embedded objects

TL;DR

This paper studies 3-D elastic scattering by penetrable obstacles with embedded objects, proving well-posedness and demonstrating unique recovery of obstacles from far-field patterns at a fixed frequency.

Contribution

It introduces a new integral equation approach to establish well-posedness and proves the unique determination of inhomogeneous obstacles from far-field data.

Findings

Well-posedness of the transmission problem established.

Unique determination of obstacles from far-field patterns proven.

Integral equation method applied to elastic scattering problems.

Abstract

This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover the obstacle by the far-field pattern measurement, is considered. It is shown that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency.