Inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium
Inverse inhomogeneous penetrable obstacle scattering problems in a stratified medium
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分层介质中逆非均匀穿透障碍物散射问题
DOI：
10.1186/s13661-017-0747-3
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发表时间：
2017-01
影响因子：
1.7
通讯作者：
Lihan Liu
中科院分区：
文献类型：
--
作者：
Guoping Zhan;Lihan Liu
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 ana prioriestimate of the solution on some part of the penetrable interfaces S i ( i = 1 , 2 ) $S_{i}\ (i = 1, 2)$, which plays an important role in the inverse scattering problems, and then we prove that both the penetrable interfaces S i ( i = 1 , 2 ) $S_{i}\ (i = 1, 2)$ and the refractive index n ( x ) $n(x)$ of the inhomogeneous penetrable obstacle Ω 2 $\Omega _{2}$ can be uniquely determined from knowledge of the far-field pattern u ∞ ( x ˆ , d ) $u^{\infty}(\widehat{x}, d)$ ( x ˆ , d ∈ S , S is the unit sphere of R 3 ) $(\widehat{x}, d \in{\mathbb{S}}, {\mathbb{S}} \text{ is the unit sphere of } {\mathbb{R}}^{3})$ for an incident plane wave u i ( x ) = e i k 1 x ⋅ d $u^{i}(x) = e^{ik_{1} x \cdot d}$ ( x ∈ R 3 ) $(x \in {\mathbb{R}}^{3})$.
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 ana prioriestimate of the solution on some part of the penetrable interfaces S i ( i = 1 , 2 ) $S_{i}\ (i = 1, 2)$, which plays an important role in the inverse scattering problems, and then we prove that both the penetrable interfaces S i ( i = 1 , 2 ) $S_{i}\ (i = 1, 2)$ and the refractive index n ( x ) $n(x)$ of the inhomogeneous penetrable obstacle Ω 2 $\Omega _{2}$ can be uniquely determined from knowledge of the far-field pattern u ∞ ( x ˆ , d ) $u^{\infty}(\widehat{x}, d)$ ( x ˆ , d ∈ S , S is the unit sphere of R 3 ) $(\widehat{x}, d \in{\mathbb{S}}, {\mathbb{S}} \text{ is the unit sphere of } {\mathbb{R}}^{3})$ for an incident plane wave u i ( x ) = e i k 1 x ⋅ d $u^{i}(x) = e^{ik_{1} x \cdot d}$ ( x ∈ R 3 ) $(x \in {\mathbb{R}}^{3})$.
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影响因子：
2.4
作者：
P. Hähner
通讯作者：
P. Hähner
DOI：
10.1515/9783110944631
发表时间：
2002-01
期刊：
--
影响因子：
--
作者：
Y. Belov
通讯作者：
Y. Belov
影响因子：
64.8
作者：
R. Kress
通讯作者：
R. Kress
影响因子：
2.1
作者：
Hu, Guanghui;Liu, Xiaodong;Zhang, Bo
通讯作者：
Zhang, Bo
DOI：
10.1007/0-387-32183-7
发表时间：
2012
期刊：
--
影响因子：
--
作者：
Michael Vogelius
通讯作者：
Michael Vogelius