Inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium

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• 作者：Guoping Zhan ; Lihan Liu
• 关键词：inverse scattering problems ; inhomogeneous penetrable obstacle ; stratified medium ; Helmholtz equation
• 刊名：Boundary Value Problems
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1495KB
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770
• 卷排序：2017

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 \(u^{i}(x) = e^{ik_{1} x \cdot d}\)\((x \in {\mathbb{R}}^{3})\).