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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Uniqueness for the inverse boundary value problem of piecewise homogeneous anisotropic elasticity in the time domain


Authors: Cătălin I. Cârstea, Gen Nakamura and Lauri Oksanen
Journal: Trans. Amer. Math. Soc. 373 (2020), 3423-3443
MSC (2010): Primary 35R30, 35L10
DOI: https://doi.org/10.1090/tran/8014
Published electronically: February 19, 2020
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Abstract: We consider the inverse boundary value problem of recovering a piecewise homogeneous elastic tensor and a piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation in the space-time domain. We derive uniqueness for identifying this tensor and density on all domains of homogeneity that may be reached from the part of the boundary where the measurements are taken by a chain of subdomains whose successive interfaces contain a curved portion.


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Additional Information

Cătălin I. Cârstea
Affiliation: School of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China
Email: catalin.carstea@gmail.com

Gen Nakamura
Affiliation: Department of Mathematics, Hokkaido University, Sapporo 060-0808, Japan
Email: gnaka@math.sci.hokudai.ac.jp

Lauri Oksanen
Affiliation: Department of Mathematics, University College London, London, United Kingdom
Email: l.oksanen@ucl.ac.uk

DOI: https://doi.org/10.1090/tran/8014
Keywords: Inverse boundary value problem; uniqueness; anisotropic elasticity.
Received by editor(s): March 24, 2019
Received by editor(s) in revised form: August 28, 2019
Published electronically: February 19, 2020
Additional Notes: Cătălin I. Cârstea is the corresponding author
The first author was partially supported by Sichuan University.
The second author was partially supported by Grant-in-Aid for Scientific Research (15K21766, 15H05740) of the Japan Society for the Promotion of Science during the research of this paper.
The third author was supported by EPSRC grants EP/P01593X/1 and EP/R002207/1.
Article copyright: © Copyright 2020 American Mathematical Society