A1 Journal article (refereed)
Uniqueness in an inverse problem of fractional elasticity (2023)
Covi, G., de Hoop, M., & Salo, M. (2023). Uniqueness in an inverse problem of fractional elasticity. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 479(2278), Article 20230474. https://doi.org/10.1098/rspa.2023.0474
JYU authors or editors
Publication details
All authors or editors: Covi, Giovanni; de Hoop, Maarten; Salo, Mikko
Journal or series: Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences
ISSN: 1364-5021
eISSN: 1471-2946
Publication year: 2023
Volume: 479
Issue number: 2278
Article number: 20230474
Publisher: The Royal Society
Publication country: United Kingdom
Publication language: English
DOI: https://doi.org/10.1098/rspa.2023.0474
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/90188
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2209.15316
Abstract
We study a nonlinear inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lamé parameters associated with a linear, isotropic fractional elasticity operator from fractional Dirichlet-to-Neumann data. In our analysis, we make use of a fractional matrix Schrödinger equation via a generalization of the so-called Liouville reduction to the case of fractional elasticity. We conclude that unique recovery is possible if the Lamé parameters agree and are constant in the exterior, and their Poisson ratios agree everywhere. Our study is motivated by the significant recent activity in the field of nonlocal elasticity.
Keywords: inverse problems; partial differential equations; elasticity (physical properties)
Free keywords: nonlocal operators; fractional Calderón problem; inverse problems; fractional elasticity; isotropic elasticity
Contributing organizations
Ministry reporting: Yes
VIRTA submission year: 2023
JUFO rating: 2