A modified transmission eigenvalue problem for scattering by a partially coated crack. (31st August 2018)

• Record Type: Journal Article
• Authors: Cogar, Samuel
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-08-31
• Subjects: inverse scattering -- nondestructive testing -- modified transmission eigenvalues -- generalized linear sampling method -- non-selfadjoint eigenvalue problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aadb20
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the detection of changes in the surface impedance of a partially coated crack, which we infer from the shift in a target signature arising from a modified interior transmission eigenvalue problem. We study this problem in a general setting in which the properties of the scattering medium are encoded in a bounded linear operator T, and we provide sufficient conditions for T that imply desirable properties of the eigenvalues of this problem. We conclude by placing scattering by a partially coated crack into this general framework and investigating the sensitivity of the associated eigenvalues to changes in the surface impedance with a series of numerical examples.