Reconstruction and uniqueness of an inverse scattering problem with impedance boundary

被引:1
作者
Liu Jijun
Cheng Jin
Gen Nakamura
机构
[1] Nanjing Normal University,Department of Mathematics
[2] Southeast University,Department of Applied Mathematics
[3] Fudan University,Department of Mathematics
[4] Hokkaido University,Department of Mathematics, Graduate School of Science
来源
Science in China Series A: Mathematics | 2002年 / 45卷
关键词
inverse scattering; inversion, uniqueness; probe method;
D O I
暂无
中图分类号
学科分类号
摘要
Consider an inverse scattering problem for a scatterer D ⊂ R3 with impedance type boundary condition. By defining the scatterer shape in a completely new way, we give a constructive method to recover the scatterer shape with unknown impedance coefficient. The uniqueness for this inverse problem is also obtained.
引用
收藏
页码:1408 / 1419
页数:11
相关论文
共 21 条
[1]  
Colton D. L.(1983)Uniqueness theorems for the inverse problem of acoustic scattering IMA J. Appl. Math. 31 253-259
[2]  
Sleeman B. D.(1998)Inverse obstacle scattering using reduced data SIAM J. Appl. Math. 59 442-454
[3]  
Kress R.(1989)On an optimization method for the full- and limited-aperture problem in inverse acoustic scattering for sound soft obstacle Inverse Problems 5 239-253
[4]  
Rundell W.(1996)A simple method for solving inverse scattering problems in the resonance region Inverse Problems 12 383-393
[5]  
Zinn A.(1995)On the numerical solution of a hypersingulr integral equation in scattering theory J. Comput. Appl. Math. 61 345-360
[6]  
Colton D. L.(1981)The determination of the surface impedance of an obstacle from measurements of the far field pattern SIAM J. Appl. Math. 41 8-15
[7]  
Kirsch A.(2000)Inverse scattering problem with impedance boundary condition J. Partial Differential Equation 13 279-288
[8]  
Kress R.(2001)Recovery of Boundary Impedance Coefficient in 2-D Media Chinese J. Numerical Mathematics and Applications 23 99-112
[9]  
Colton D. L.(1993)The determination of the surface impedance of an obstacle Proc. Edingburgh Math. Soc. 36 1-15
[10]  
Liu J. J.(1985)An inverse acoustic scattering problem for an obstacle with an impedance boundary condition J. Math. Anal. Appl. 105 333-356