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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.07415 |
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| _version_ | 1866910364386459648 |
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| author | Chaumont-Frelet, T. Nicaise, S. |
| author_facet | Chaumont-Frelet, T. Nicaise, S. |
| contents | We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $ω$ and ratio of the Lamé parameters $λ/μ$ may both be large. We derive stability estimates controlling the norm of the solution by the norm of the right-hand side up to a fully-explicit constant. Crucially, under natural assumptions on the domain and coefficients, this constant increases linearly with $ω$ and is uniform in the ratio $λ/μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07415 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials Chaumont-Frelet, T. Nicaise, S. Analysis of PDEs We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $ω$ and ratio of the Lamé parameters $λ/μ$ may both be large. We derive stability estimates controlling the norm of the solution by the norm of the right-hand side up to a fully-explicit constant. Crucially, under natural assumptions on the domain and coefficients, this constant increases linearly with $ω$ and is uniform in the ratio $λ/μ$. |
| title | Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.07415 |