American Institute of Mathematical Sciences

Advanced
March  2008, 9(2): 375-396. doi: 10.3934/dcdsb.2008.9.375

Uniqueness in determining multiple polygonal scatterers of mixed type

Hongyu Liu 1, and  Jun Zou 2,

1. 

Department of Mathematics, University of Washington, Box 354350, Seattle WA 98195, United States
2. 

Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Received  July 2007 Revised  November 2007 Published  December 2007

We prove that a polygonal scatterer in $\mathbb{R}^2$, possibly consisting of finitely many sound-soft and sound-hard polygons, is uniquely determined by a single far-field measurement.
Keywords: polygonal scatterers, mixed type., Inverse obstacle scattering, uniqueness.
Mathematics Subject Classification: Primary: 78A46, 35R30; Secondary: 76Q05, 35P2.
Citation: Hongyu Liu, Jun Zou. Uniqueness in determining multiple polygonal scatterers of mixed type. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 375-396. doi: 10.3934/dcdsb.2008.9.375
[1]

Jun Lai, Ming Li, Peijun Li, Wei Li. A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers. Inverse Problems & Imaging, 2018, 12 (3) : 635-665. doi: 10.3934/ipi.2018027
[2]

Jianli Xiang, Guozheng Yan. The uniqueness of the inverse elastic wave scattering problem based on the mixed reciprocity relation. Inverse Problems & Imaging, 2021, 15 (3) : 539-554. doi: 10.3934/ipi.2021004
[3]

Johannes Elschner, Guanghui Hu, Masahiro Yamamoto. Uniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type. Inverse Problems & Imaging, 2015, 9 (1) : 127-141. doi: 10.3934/ipi.2015.9.127
[4]

Peijun Li, Xiaokai Yuan. Inverse obstacle scattering for elastic waves in three dimensions. Inverse Problems & Imaging, 2019, 13 (3) : 545-573. doi: 10.3934/ipi.2019026
[5]

Masaru Ikehata, Esa Niemi, Samuli Siltanen. Inverse obstacle scattering with limited-aperture data. Inverse Problems & Imaging, 2012, 6 (1) : 77-94. doi: 10.3934/ipi.2012.6.77
[6]

Lu Zhao, Heping Dong, Fuming Ma. Inverse obstacle scattering for acoustic waves in the time domain. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021037
[7]

Johannes Elschner, Guanghui Hu. Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems & Imaging, 2011, 5 (4) : 793-813. doi: 10.3934/ipi.2011.5.793
[8]

Brian Sleeman. The inverse acoustic obstacle scattering problem and its interior dual. Inverse Problems & Imaging, 2009, 3 (2) : 211-229. doi: 10.3934/ipi.2009.3.211
[9]

Mourad Sini, Nguyen Trung Thành. Inverse acoustic obstacle scattering problems using multifrequency measurements. Inverse Problems & Imaging, 2012, 6 (4) : 749-773. doi: 10.3934/ipi.2012.6.749
[10]

Christodoulos E. Athanasiadis, Vassilios Sevroglou, Konstantinos I. Skourogiannis. The inverse electromagnetic scattering problem by a mixed impedance screen in chiral media. Inverse Problems & Imaging, 2015, 9 (4) : 951-970. doi: 10.3934/ipi.2015.9.951
[11]

Masaru Ikehata. The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain. Inverse Problems & Imaging, 2016, 10 (1) : 131-163. doi: 10.3934/ipi.2016.10.131
[12]

Bastian Gebauer, Nuutti Hyvönen. Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem. Inverse Problems & Imaging, 2008, 2 (3) : 355-372. doi: 10.3934/ipi.2008.2.355
[13]

Giorgio Menegatti, Luca Rondi. Stability for the acoustic scattering problem for sound-hard scatterers. Inverse Problems & Imaging, 2013, 7 (4) : 1307-1329. doi: 10.3934/ipi.2013.7.1307
[14]

Xiaoxu Xu, Bo Zhang, Haiwen Zhang. Uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data at a fixed frequency. Inverse Problems & Imaging, 2020, 14 (3) : 489-510. doi: 10.3934/ipi.2020023
[15]

T. J. Christiansen. Resonances and balls in obstacle scattering with Neumann boundary conditions. Inverse Problems & Imaging, 2008, 2 (3) : 335-340. doi: 10.3934/ipi.2008.2.335
[16]

Masaya Maeda, Hironobu Sasaki, Etsuo Segawa, Akito Suzuki, Kanako Suzuki. Scattering and inverse scattering for nonlinear quantum walks. Discrete & Continuous Dynamical Systems, 2018, 38 (7) : 3687-3703. doi: 10.3934/dcds.2018159
[17]

Francesco Demontis, Cornelis Van der Mee. Novel formulation of inverse scattering and characterization of scattering data. Conference Publications, 2011, 2011 (Special) : 343-350. doi: 10.3934/proc.2011.2011.343
[18]

Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems & Imaging, 2009, 3 (3) : 537-550. doi: 10.3934/ipi.2009.3.537
[19]

Siamak RabieniaHaratbar. Inverse scattering and stability for the biharmonic operator. Inverse Problems & Imaging, 2021, 15 (2) : 271-283. doi: 10.3934/ipi.2020064
[20]

Lu Zhao, Heping Dong, Fuming Ma. Time-domain analysis of forward obstacle scattering for elastic wave. Discrete & Continuous Dynamical Systems - B, 2021, 26 (8) : 4111-4130. doi: 10.3934/dcdsb.2020276

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (34)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences