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arXiv · 2511.05711

Factorization method for the biharmonic scattering problem for an absorbing penetrable scatterer

Rafael Ceja Ayala·Isaac Harris·General Ozochiawaeze
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Abstract

This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that the plate thickness is small compared to the wavelength of the incident wave, the propagation of flexural perturbations is modeled by the two--dimensional biharmonic wave equation in the frequency domain. Within this setting, we provide a rigorous justification of the factorization method and demonstrate that it yields a binary criterion for distinguishing whether a sampling point lies inside or outside the scatterer, using only the spectral data of the far--field operator. In addition, we numerically analyze the Born approximation for weak scatterers in this biharmonic scattering context and compute the relative error against exact far--field data for sample weak scatterers, thereby quantifying its validity as a limited but useful approximation.

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Rafael Ceja Ayala, Isaac Harris, General Ozochiawaeze. 2025-11-07. Factorization method for the biharmonic scattering problem for an absorbing penetrable scatterer. https://arxiv.org/abs/2511.05711

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