February  2008, 2(1): 151-165. doi: 10.3934/ipi.2008.2.151

On uniqueness of obstacles and boundary conditions from restricted dynamical and scattering data

1. 

Wichita State University, 1845 Fairmount, Wichita, KS, 67260-0033

Received  May 2007 Revised  June 2007 Published  January 2008

We show uniqueness of a (time independent) domain $D$ and of an impedance type boundary condition from either dynamical or scattering data at many frequencies. We assume that the additonal boundary (scattering) data are given for one set of boundary data or for one incident direction. In case of general domain and finite (sharp) observation time we assume Neumann boundary condition on $\partial D$ and for polygonal $D$ we can handle more general case. If the data are available for all times we show uniqueness of the most general impedance boundary condition by using continuation of the corresponding scattering data into complex domain and modifying the Schiffer's argument.
Citation: Victor Isakov. On uniqueness of obstacles and boundary conditions from restricted dynamical and scattering data. Inverse Problems & Imaging, 2008, 2 (1) : 151-165. doi: 10.3934/ipi.2008.2.151
[1]

Tan Bui-Thanh, Omar Ghattas. Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions. Inverse Problems & Imaging, 2013, 7 (4) : 1139-1155. doi: 10.3934/ipi.2013.7.1139

[2]

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

[3]

Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems & Imaging, 2008, 2 (4) : 577-586. doi: 10.3934/ipi.2008.2.577

[4]

Gabriel Katz. Causal holography in application to the inverse scattering problems. Inverse Problems & Imaging, 2019, 13 (3) : 597-633. doi: 10.3934/ipi.2019028

[5]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part II: Posterior convergence for approximated unknowns. Inverse Problems & Imaging, 2012, 6 (2) : 267-287. doi: 10.3934/ipi.2012.6.267

[6]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part I: Posterior distributions. Inverse Problems & Imaging, 2012, 6 (2) : 215-266. doi: 10.3934/ipi.2012.6.215

[7]

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

[8]

Laurent Bourgeois, Houssem Haddar. Identification of generalized impedance boundary conditions in inverse scattering problems. Inverse Problems & Imaging, 2010, 4 (1) : 19-38. doi: 10.3934/ipi.2010.4.19

[9]

Frederic Weidling, Thorsten Hohage. Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems. Inverse Problems & Imaging, 2017, 11 (1) : 203-220. doi: 10.3934/ipi.2017010

[10]

Colin Guillarmou, Antônio Sá Barreto. Inverse problems for Einstein manifolds. Inverse Problems & Imaging, 2009, 3 (1) : 1-15. doi: 10.3934/ipi.2009.3.1

[11]

Sergei Avdonin, Pavel Kurasov. Inverse problems for quantum trees. Inverse Problems & Imaging, 2008, 2 (1) : 1-21. doi: 10.3934/ipi.2008.2.1

[12]

Maciej Zworski. A remark on inverse problems for resonances. Inverse Problems & Imaging, 2007, 1 (1) : 225-227. doi: 10.3934/ipi.2007.1.225

[13]

Guanghui Hu, Peijun Li, Xiaodong Liu, Yue Zhao. Inverse source problems in electrodynamics. Inverse Problems & Imaging, 2018, 12 (6) : 1411-1428. doi: 10.3934/ipi.2018059

[14]

Michael Herty, Giuseppe Visconti. Kinetic methods for inverse problems. Kinetic & Related Models, 2019, 12 (5) : 1109-1130. doi: 10.3934/krm.2019042

[15]

Guangsheng Wei, Hong-Kun Xu. On the missing bound state data of inverse spectral-scattering problems on the half-line. Inverse Problems & Imaging, 2015, 9 (1) : 239-255. doi: 10.3934/ipi.2015.9.239

[16]

Kaitlyn (Voccola) Muller. A reproducing kernel Hilbert space framework for inverse scattering problems within the Born approximation. Inverse Problems & Imaging, 2019, 13 (6) : 1327-1348. doi: 10.3934/ipi.2019058

[17]

Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems & Imaging, 2007, 1 (1) : 77-93. doi: 10.3934/ipi.2007.1.77

[18]

Masoumeh Dashti, Stephen Harris, Andrew Stuart. Besov priors for Bayesian inverse problems. Inverse Problems & Imaging, 2012, 6 (2) : 183-200. doi: 10.3934/ipi.2012.6.183

[19]

Xiaosheng Li, Gunther Uhlmann. Inverse problems with partial data in a slab. Inverse Problems & Imaging, 2010, 4 (3) : 449-462. doi: 10.3934/ipi.2010.4.449

[20]

Sergei A. Avdonin, Sergei A. Ivanov, Jun-Min Wang. Inverse problems for the heat equation with memory. Inverse Problems & Imaging, 2019, 13 (1) : 31-38. doi: 10.3934/ipi.2019002

2018 Impact Factor: 1.469

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]