Inverse scattering for three-dimensional quasi-linear biharmonic operator-Reference-Cited by-同舟云学术

Inverse scattering for three-dimensional quasi-linear biharmonic operator

Published:2022-01-06 Issue:3 Volume:30 Page:379-393
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Harju Markus¹,Kultima Jaakko²^ORCID,Serov Valery³

Affiliation:

1. Biomimetics and Intelligent Systems Group , University of Oulu , P.O. BOX 8000 , Oulu 90014 , Finland

2. Research Unit of Mathematical Sciences , University of Oulu , P.O. BOX 3000 , Oulu 90014 , Finland

3. Research Unit of Mathematical Sciences , University of Oulu , P.O. BOX 3000 , Oulu 90014 , Finland ; and Moscow Centre of Fundamental and Applied Mathematics – Lomonosov Moscow State University, Moscow, Russia

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0069/pdf

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