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Recovering an obstacle using integral equations
An estimate for the free Helmholtz equation that scales
1.  Department of Mathematics, University of Washington, Seattle, Washington 981953540, United States 
[1] 
Michael V. Klibanov. A phaseless inverse scattering problem for the 3D Helmholtz equation. Inverse Problems and Imaging, 2017, 11 (2) : 263276. doi: 10.3934/ipi.2017013 
[2] 
Masaya Maeda, Hironobu Sasaki, Etsuo Segawa, Akito Suzuki, Kanako Suzuki. Scattering and inverse scattering for nonlinear quantum walks. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 36873703. doi: 10.3934/dcds.2018159 
[3] 
Francesco Demontis, Cornelis Van der Mee. Novel formulation of inverse scattering and characterization of scattering data. Conference Publications, 2011, 2011 (Special) : 343350. doi: 10.3934/proc.2011.2011.343 
[4] 
John C. Schotland, Vadim A. Markel. FourierLaplace structure of the inverse scattering problem for the radiative transport equation. Inverse Problems and Imaging, 2007, 1 (1) : 181188. doi: 10.3934/ipi.2007.1.181 
[5] 
WeiKang Xun, ShouFu Tian, TianTian Zhang. Inverse scattering transform for the integrable nonlocal LakshmananPorsezianDaniel equation. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021259 
[6] 
Yuan Li, ShouFu Tian. Inverse scattering transform and soliton solutions of an integrable nonlocal Hirota equation. Communications on Pure and Applied Analysis, 2022, 21 (1) : 293313. doi: 10.3934/cpaa.2021178 
[7] 
Leonardo Marazzi. Inverse scattering on conformally compact manifolds. Inverse Problems and Imaging, 2009, 3 (3) : 537550. doi: 10.3934/ipi.2009.3.537 
[8] 
Siamak RabieniaHaratbar. Inverse scattering and stability for the biharmonic operator. Inverse Problems and Imaging, 2021, 15 (2) : 271283. doi: 10.3934/ipi.2020064 
[9] 
Daniel Bouche, Youngjoon Hong, ChangYeol Jung. Asymptotic analysis of the scattering problem for the Helmholtz equations with high wave numbers. Discrete and Continuous Dynamical Systems, 2017, 37 (3) : 11591181. doi: 10.3934/dcds.2017048 
[10] 
Fenglong Qu, Jiaqing Yang. On recovery of an inhomogeneous cavity in inverse acoustic scattering. Inverse Problems and Imaging, 2018, 12 (2) : 281291. doi: 10.3934/ipi.2018012 
[11] 
Peter Monk, Jiguang Sun. Inverse scattering using finite elements and gap reciprocity. Inverse Problems and Imaging, 2007, 1 (4) : 643660. doi: 10.3934/ipi.2007.1.643 
[12] 
Johannes Elschner, Guanghui Hu. Uniqueness in inverse transmission scattering problems for multilayered obstacles. Inverse Problems and Imaging, 2011, 5 (4) : 793813. doi: 10.3934/ipi.2011.5.793 
[13] 
Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems and Imaging, 2008, 2 (4) : 577586. doi: 10.3934/ipi.2008.2.577 
[14] 
Peijun Li, Xiaokai Yuan. Inverse obstacle scattering for elastic waves in three dimensions. Inverse Problems and Imaging, 2019, 13 (3) : 545573. doi: 10.3934/ipi.2019026 
[15] 
Fang Zeng. Extended sampling method for interior inverse scattering problems. Inverse Problems and Imaging, 2020, 14 (4) : 719731. doi: 10.3934/ipi.2020033 
[16] 
Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems and Imaging, 2009, 3 (4) : 551565. doi: 10.3934/ipi.2009.3.551 
[17] 
Gabriel Katz. Causal holography in application to the inverse scattering problems. Inverse Problems and Imaging, 2019, 13 (3) : 597633. doi: 10.3934/ipi.2019028 
[18] 
Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems and Imaging, 2013, 7 (1) : 291303. doi: 10.3934/ipi.2013.7.291 
[19] 
Qinghua Wu, Guozheng Yan. The factorization method for a partially coated cavity in inverse scattering. Inverse Problems and Imaging, 2016, 10 (1) : 263279. doi: 10.3934/ipi.2016.10.263 
[20] 
Masaru Ikehata, Esa Niemi, Samuli Siltanen. Inverse obstacle scattering with limitedaperture data. Inverse Problems and Imaging, 2012, 6 (1) : 7794. doi: 10.3934/ipi.2012.6.77 
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