Journal Article

FZJ-2025-03588

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png On the transmission eigenvalues for scattering by a clamped planar region

Harris, I. (Corresponding author) ; Kleefeld, A.FZJ* ; Lee, H.

2026
AIMS

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Please use a persistent id in citations: doi:10.3934/ipi.2025038

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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2025

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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