Open AccessBoundary determination of electromagnetic and Lamé parameters with corrupted data
Author(s) -
Pedro Caro,
Ru-Yu Lai,
Yi-Hsuan Lin,
Ting Zhou
Publication year - 2021
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021033
Subject(s) - mathematical analysis , maxwell's equations , isotropy , inverse problem , elasticity (physics) , boundary value problem , mathematics , lipschitz continuity , permittivity , boundary (topology) , inverse , physics , geometry , optics , dielectric , thermodynamics , optoelectronics
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the electromagnetic parameters and the Lamé moduli for these two systems from the corresponding boundary measurements. In a first step we reconstruct Lipschitz magnetic permeability, electric permittivity and conductivity on the surface from the ideal boundary measurements. Then, we study inverse problems for Maxwell equations and the isotropic elasticity system assuming that the data contains measurement errors. For both systems, we provide explicit formulas to reconstruct the parameters on the boundary as well as its rate of convergence formula.