Work

On the transmission eigenvalues for scattering by a clamped planar region

Year: 2025

Type: article

Abstract: In this paper, we consider a new transmission eigenvalue problem derived from the scattering by a clamped cavity in a thin elastic material. Scattering in a thin elastic material can be modeled by the Kirchhoff–Love infinite plate problem. This results in a biharmonic scattering problem that can be handled by operator splitting. The main novelty of this transmission eigenvalue problem is that it is posed in all of $ \mathbb{R}^2 $. This adds analytical and computational difficulties in studying this eigenvalue problem. Here, we prove that the eigenvalues can be recovered from the far field data as well as discreteness of the transmission eigenvalues. We provide some numerical experiments via boundary integral equations to demonstrate the theoretical results. We also conjecture monotonicity with respect to the measure of the scatterer from our numerical experiments.

Source: Inverse Problems and Imaging

DOI: 10.3934/ipi.2025038

Authors: Isaac Harris, Andreas Kleefeld, Heejin Lee

Institutions: Purdue University West Lafayette, Forschungszentrum Jülich, Jülich Supercomputing Centre, Duke Kunshan University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Award: Direct and Inverse Scattering in Biharmonic Waves: Analysis and Computation