Uniqueness in an inverse problem of fractional elasticity
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
Julkaistu sarjassa
Proceedings of the Royal Society A : Mathematical, Physical and Engineering SciencesPäivämäärä
2023Oppiaine
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsTekijänoikeudet
© Authors 2023
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.
Julkaisija
The Royal SocietyISSN Hae Julkaisufoorumista
1364-5021Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/193429464
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Inverse problems for a fractional conductivity equation
Covi, Giovanni (Pergamon Press, 2020)This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, ... -
The Calderón Problem for the Fractional Wave Equation : Uniqueness and Optimal Stability
Kow, Pu-Zhao; Lin, Yi-Hsuan; Wang, Jenn-Nan (Society for Industrial & Applied Mathematics (SIAM), 2022)We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and ... -
Inverse problems for elliptic equations with fractional power type nonlinearities
Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu (Elsevier, 2022)We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain ... -
The Calderón problem for the fractional Schrödinger equation
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther (Mathematical Sciences Publishers, 2020)We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness ... -
Quantitative approximation properties for the fractional heat equation
Rüland, Angkana; Salo, Mikko (American Institute of Mathematical Sciences, 2020)In this article we analyse quantitative approximation properties of a certain class of nonlocal equations: Viewing the fractional heat equation as a model problem, which involves both local and nonlocal pseudodifferential ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.