Radiating and non-radiating sources in elasticity
Blåsten, E., & Lin, Y.-H. (2019). Radiating and non-radiating sources in elasticity. Inverse Problems, 35(1), 015005. https://doi.org/10.1088/1361-6420/aae99e
Published inInverse Problems
© 2018 IOP Publishing Ltd
In this work, we study the inverse source problem of a fixed frequency for the Navier equation. We investigate non-radiating external forces. If the support of such a force has a convex or non-convex corner or edge on its boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: an energy identity and a new type of exponential solution for the Navier equation.
PublisherInstitute of Physics
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingThe authors appreciate Professor Ikehata and the anonymous referees for some useful comments to improve this work. Y-H Lin is partially supported by the Academy of Finland, under the project number 309963.
Showing items with similar title or keywords.
Rüland, Angkana; Salo, Mikko (Oxford University Press, 2019)In this short note, we provide a quantitative version of the classical Runge approximation property for second-order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We ...
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (Elsevier, 2021)We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for ...
Salo, Mikko (MDPI AG, 2020)This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, ...
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 ...
Meroño, Cristóbal J.; Potenciano-Machado, Leyter; Salo, Mikko (Springer Science and Business Media LLC, 2021)We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely ...