文摘
In this paper we study the inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium. On the basis of the uniqueness and existence of solutions for the direct scattering by an inhomogeneous penetrable obstacle in a stratified medium, we first establish an a priori estimate of the solution on some part of the penetrable interfaces \(S_{i}\ (i = 1, 2)\), which plays an important role in the inverse scattering problems, and then we prove that both the penetrable interfaces \(S_{i}\ (i = 1, 2)\) and the refractive index \(n(x)\) of the inhomogeneous penetrable obstacle \(\Omega _{2}\) can be uniquely determined from knowledge of the far-field pattern \(u^{\infty}(\widehat{x}, d)\)\((\widehat{x}, d \in{\mathbb{S}}, {\mathbb{S}} \text{ is the unit sphere of } {\mathbb{R}}^{3})\) for an incident plane wave \(u^{i}(x) = e^{ik_{1} x \cdot d}\)\((x \in {\mathbb{R}}^{3})\).
