On the asymptotic behavior of a diffraction problem with a thin layer
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918105802866688 |
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| author | Acampora, Paolo Cristoforoni, Emanuele |
| author_facet | Acampora, Paolo Cristoforoni, Emanuele |
| contents | We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set $Ω$ and a thin layer $Σ$ locally described by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partialΩ$, and $\varepsilon$ is the ellipticity constant of the differential operator in the thin layer $Σ$. We study the problem in the limit for $\varepsilon$ going to zero and prove a first-order asymptotic development by $Γ$-convergence of the associated energy functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotic behavior of a diffraction problem with a thin layer Acampora, Paolo Cristoforoni, Emanuele Analysis of PDEs 49J45, 35J25, 35B40, 80A19 We investigate the behavior of the solution to an elliptic diffraction problem in the union of a smooth set $Ω$ and a thin layer $Σ$ locally described by $\varepsilon h$, where $h$ is a positive function defined on the boundary $\partialΩ$, and $\varepsilon$ is the ellipticity constant of the differential operator in the thin layer $Σ$. We study the problem in the limit for $\varepsilon$ going to zero and prove a first-order asymptotic development by $Γ$-convergence of the associated energy functional. |
| title | On the asymptotic behavior of a diffraction problem with a thin layer |
| topic | Analysis of PDEs 49J45, 35J25, 35B40, 80A19 |
| url | https://arxiv.org/abs/2404.12054 |