University of Oulu

Teemu Tyni, Valery Serov. Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line. Inverse Problems & Imaging, 2019, 13 (1) : 159-175. doi: 10.3934/ipi.2019009

Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line

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Author: Tyni, Teemu1; Serov, Valery1
Organizations: 1Department of Mathematical Sciences, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: American Institute of Mathematical Sciences, 2019
Publish Date: 2020-02-28


We consider an inverse scattering problem of recovering the unknown coefficients of quasi-linearly perturbed biharmonic operator on the line. 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 that the inverse Born approximation can be used to recover some essential information about the unknown coefficients from the knowledge of the reflection coefficient. This information is the jump discontinuities and the local singularities of the coefficients.

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Series: Inverse problems and imaging
ISSN: 1930-8337
ISSN-E: 1930-8345
ISSN-L: 1930-8337
Volume: 13
Issue: 1
Pages: 159 - 175
DOI: 10.3934/ipi.2019009
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This work was supported by the Academy of Finland (application number 250215, the Centres of Excellence in Research 2012-2017 and application number 312123, the Centre of Excellence of Inverse Modelling and Imaging (2018-2025)). The first author was supported by the Doctoral Programme in Exact Sciences at the University of Oulu, Finland.
Copyright information: Inverse Problems & Imaging © 2019 Published by AIMS. All rights reserved.