Uniqueness in determining a convex polygonal source of an elastic body

TL;DR

This paper proves that a convex polygonal elastic source can be uniquely identified from a single far field measurement using corner singularity analysis, advancing inverse elastic source theory.

Contribution

It introduces a novel approach using corner singularity analysis to achieve uniqueness in identifying convex polygonal sources in elastic bodies.

Findings

Unique determination of convex polygonal sources from one measurement

Extension of corner scattering theory for non-convex domains

New analytical techniques for inverse elastic problems

Abstract

In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our approach relies on the corner singularity analysis of solutions to the inhomogeneous Navier equation with a source term in a sector. This paper also contributes to corner scattering theory for the Navier equation in an non-convex domain.