Journal Article

FZJ-2025-04907

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

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

2025
Inst. Bristol [u.a.]

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Please use a persistent id in citations: doi:10.1088/1361-6420/ae259b  doi:10.34734/FZJ-2025-04907

Abstract: In this paper, we study the so-called clamped transmission eigenvalue problem. This is a new transmission eigenvalue problem that is derived from the scattering of an impenetrable clamped obstacle in a thin elastic plate. The scattering problem is modeled by a biharmonic wave operator given by the Kirchhoff-Love infinite plate problem in the frequency domain. These scattering problems have not been studied to the extent of other models. Unlike other transmission eigenvalue problems, the problem studied here is a system of homogeneous PDEs defined in all of $\mathbb{R}^2$ . This provides unique analytical and computational difficulties when studying the clamped transmission eigenvalue problem. We are able to prove that there exist infinitely many real clamped transmission eigenvalues. This is done by studying the equivalent variational formulation. We also investigate the relationship of the clamped transmission eigenvalues to the Dirichlet and Neumann eigenvalues of the negative Laplacian for the bounded scattering obstacle.

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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 ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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