Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908855573676032 |
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| author | Derbissaly, Bauyrzhan Lamberti, Pier Domenico |
| author_facet | Derbissaly, Bauyrzhan Lamberti, Pier Domenico |
| contents | In this paper, we investigate the asymptotic behavior of the eigenvalues and eigenfunctions of a biharmonic Steklov problem defined on a thin domain in the $n$ dimensional Euclidean space degenerating to a segment. For $n=2$ the problem models the vibrations of a thin elastic plate with cross section represented by the given domain and mass concentrated on a free boundary. The problem under consideration depends on a parameter $σ$ that in the theory of elastic plates represents the Poisson ratio of the material. Our analysis points out a distortion in the limiting problem depending on $σ$ and the space dimension $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains Derbissaly, Bauyrzhan Lamberti, Pier Domenico Analysis of PDEs Spectral Theory In this paper, we investigate the asymptotic behavior of the eigenvalues and eigenfunctions of a biharmonic Steklov problem defined on a thin domain in the $n$ dimensional Euclidean space degenerating to a segment. For $n=2$ the problem models the vibrations of a thin elastic plate with cross section represented by the given domain and mass concentrated on a free boundary. The problem under consideration depends on a parameter $σ$ that in the theory of elastic plates represents the Poisson ratio of the material. Our analysis points out a distortion in the limiting problem depending on $σ$ and the space dimension $n$. |
| title | Asymptotic behavior and spectral distortion for biharmonic Steklov problems on thin domains |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2602.23818 |