2025/10/09 by Rafael Ceja Ayala, Ayala, Rafael Ceja, Isaac Harris +3
Mathematics · Engineering · #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #Microwave Imaging and Scattering Analysis
paper · pdf · doi:10.48550/arxiv.2510.08444
In this paper, we provide an analytical study of the transmission eigenvalue problem in the context of biharmonic scattering with a penetrable obstacle. We will assume that the underlying physical model is given by an infinite elastic two--dimensional Kirchhoff--Love plate in ℝ2, where the plate's thickness is small relative to the wavelength of the incident wave. In previous studies, transmission eigenvalues have been studied for acoustic scattering, whereas in this case, we consider biharmonic scattering. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the refractive index. We are able to prove the monotonicity of the first transmission eigenvalue with respect to the refractive index. Lastly, we provide numerical experiments to validate the theoretical work.