Uniqueness of scatterer in inverse acoustic obstacle scattering with a single incident plane wave

Abstract

In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic scattering amplitude $A(\beta ,{\alpha }_0,k_0)$, known for all $\beta \in {\mathbb{S}}^2$, where ${\mathbb{S}}^2$ is the unit sphere in ${\mathbb{R}}^3$, ${\alpha }_0\in {\mathbb{S}}^2$ is fixed, $k_0>0$ is fixed, determines the obstacle $D$ and the boundary condition on $\partial D$ uniquely (The boundary condition on $\partial D$ is either the Dirichlet, or Neumann, or the impedance one).

The proof of main theorem in this paper has a gap

References in corpus (2)

• Recovery of an embedded obstacle and its surrounding medium by formally-determined scattering data
• On uniqueness in the inverse obstacle problem via the positive supersolutions of the Helmholtz equation

Cited by in corpus (1)

• Uniqueness in inverse elastic scattering with one incident wave