Work

Analysis of the transmission eigenvalue problem for biharmonic scattering considering penetrable scatterers

Year: 2025

Type: preprint

Abstract: 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 $\mathbb{R}^2$, 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.08444

Authors: Ayala, Rafael Ceja, Harris, Isaac, Kleefeld, Andreas

Institutions: Arizona State University, Purdue University West Lafayette, Forschungszentrum Jülich, Jülich Supercomputing Centre, FH Aachen

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Qualitative reconstruction methods for inverse Biharmonic scattering, Direct and Inverse Scattering in Biharmonic Waves: Analysis and Computation

OpenAlex ID: W4416385181

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