Uniqueness in inverse elastic scattering with one incident wave

TL;DR

This paper proves that the shape and boundary condition of an obstacle in elastic scattering can be uniquely determined from a single far field pattern of a fixed incident wave, solving a longstanding open problem.

Contribution

It establishes the uniqueness of obstacle shape and boundary condition in inverse elastic scattering using only one incident wave at fixed frequency and direction.

Findings

Unique determination of obstacle shape from one far field pattern

Boundary condition (Dirichlet, Neumann, Robin) also uniquely identified

Addresses a longstanding open problem in elastic scattering theory

Abstract

In this paper, we give a positive answer to a longstanding open problem for determining the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic elastic wave. We show that the elastic far field pattern by an incoming plane wave with a fixed frequency, a fixed incident direction and a fixed polarization determines the obstacle $D$ and the boundary condition on $\partial D$ uniquely. The boundary condition on $\partial D$ is either the Dirichlet, or the Neumann, or the Robin one.