Reconstruction of penetrable inclusions in elastic waves by boundary measurements

TL;DR

This paper advances the reconstruction of penetrable inclusions in elastic bodies using boundary measurements by applying and extending the enclosure method with complex geometrical optics solutions, allowing for less regular boundary assumptions.

Contribution

It adapts Sini and Yoshida's approach to elastic waves, reducing boundary regularity assumptions to mere continuity for reconstructing inclusions.

Findings

Boundaries of inclusions can be assumed to be only continuous.

The enclosure method effectively reconstructs inclusions with minimal boundary regularity.

The approach extends previous methods by removing technical assumptions.

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.