Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces

被引：3

作者：

Mantile, Andrea ^{[1
]}

Posilicano, Andrea ^{[2
]}

Sini, Mourad ^{[3
]}

机构：

[1] Univ Reims, Lab Math, CNRS, FR3399, Moulin Housse BP 1039, F-51687 Reims, France

[2] Univ Insubria, DiSAT, Sez Matemat, Via Valleggio 11, I-22100 Como, Italy

[3] Austrian Acad Sci, RICAM, Altenbergerstr 69, A-4040 Linz, Austria

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 265卷 / 09期

基金：

奥地利科学基金会;

关键词：

Inverse scattering; Acoustic equation; Schrodinger operators; GLOBAL UNIQUENESS; CONDUCTIVITIES; OPERATORS; EQUATION; FORMULA;

D O I：

10.1016/j.jde.2018.05.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Sigma subset of Gamma = partial derivative Omega, where Omega is a bounded open subset of R-3 with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrodinger operators with singular delta-type potential supported on the surface Gamma and of strength alpha is an element of L-p (Gamma), p > 2. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：4101 / 4132

页数：32

共 50 条

[31] Zeros of the Bessel and spherical Bessel functions and their applications for uniqueness in inverse acoustic obstacle scattering
Liu, Hongyu
Zou, Jun
IMA JOURNAL OF APPLIED MATHEMATICS, 2007, 72 (06) : 817 - 831
[32] Uniqueness for inverse conductivity and transmission problems in the class of Lipschitz domains
Mitrea, D
Mitrea, M
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1998, 23 (7-8) : 1419 - 1448
[33] UNIQUENESS OF A SOLUTION OF AN INVERSE SCATTERING PROBLEM
STEPANOV, VN
DIFFERENTIAL EQUATIONS, 1982, 18 (04) : 482 - 487
[34] On uniqueness in inverse scattering problem for gratings
Ammari, H
Kallel, L
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (02): : 187 - 190
[35] Uniqueness of the inverse conductive scattering problem
Natl Univ of Singapore, Singapore, Singapore
Comput Math Appl, 8 (53-57):
[36] Uniqueness of the inverse conductive scattering problem
Yan, G
Pang, PYH
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (08) : 53 - 57
[37] ON UNIQUENESS IN THE INVERSE TRANSMISSION SCATTERING PROBLEM
ISAKOV, V
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1990, 15 (11) : 1565 - 1587
[38] ELECTROMAGNETIC SCATTERING BY UNBOUNDED ROUGH SURFACES
Li, Peijun
Wu, Haijun
Zheng, Weiying
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 43 (03) : 1205 - 1231
[39] ELASTIC SCATTERING BY UNBOUNDED ROUGH SURFACES
Elschner, Johannes
Hu, Guanghui
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (06) : 4101 - 4127
[40] Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains
Behrndt, Jussi
Rohleder, Jonathan
INVERSE PROBLEMS, 2020, 36 (03)

← 1 2 3 4 5 →