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

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.