University of Oulu

Harju, M., Kultima, J. & Serov, V. (2022). Inverse scattering for three-dimensional quasi-linear biharmonic operator. Journal of Inverse and Ill-posed Problems, 30(3), 379-393.

Inverse scattering for three-dimensional quasi-linear biharmonic operator

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Author: Harju, Markus1; Kultima, Jaakko2; Serov, Valery2,3
Organizations: 1Biomimetics and Intelligent Systems Group, University of Oulu, P.O. BOX 8000, Oulu 90014, Finland
2Research Unit of Mathematical Sciences, University of Oulu, P.O. BOX 3000, Oulu 90014, Finland
3Moscow Centre of Fundamental and Applied Mathematics – Lomonosov Moscow State University, Moscow, Russia
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.6 MB)
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Language: English
Published: De Gruyter, 2022
Publish Date: 2023-03-27


We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

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Series: Journal of inverse and ill-posed problems
ISSN: 0928-0219
ISSN-E: 1569-3945
ISSN-L: 0928-0219
Volume: 30
Issue: 3
Pages: 379 - 393
DOI: 10.1515/jiip-2020-0069
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This work was supported by the Academy of Finland (application number 312123, the Centre of Excellence of Inverse Modelling and Imaging 2018-2025) and by Moscow Centre of Fundamental and Applied Mathematics – MSU, Russia.
Academy of Finland Grant Number: 312123
Detailed Information: 312123 (Academy of Finland Funding decision)
Copyright information: © 2022 Walter de Gruyter GmbH, Berlin/Boston.