Heejin Lee, Purdue University
Authors: Fioralba Cakoni, Heejin Lee, Peter Monk and Yangwen Zhang
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]

In this talk, we consider the inverse problem of determining the structural properties of a thin anisotropic and dissipative inhomogeneity from scattering data. In the asymptotic limit, as the thickness goes to zero, the thin inhomogeneity is modeled by an open m-1 manifold(here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second-order surface differential operator. We show that all the surface coefficients are uniquely determined from far-field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data. Changes in the measured eigenvalues are used to identify changes in the coefficients without using the governing equations that model the healthy screen. In our investigation, the shape of the screen is known since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach. This is joint work with Fioralba Cakoni, Peter Monk, and Yangwen Zhang.

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