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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2507.16546 |
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| _version_ | 1866915404746588160 |
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| author | Balehouane, Abdelkhalek Kasri, Hicham Kechkar, Rokia |
| author_facet | Balehouane, Abdelkhalek Kasri, Hicham Kechkar, Rokia |
| contents | In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $Ω$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to be locally distributed and satisfies suitable assumptions. The smooth boundary of $Ω$ is $Γ=Γ_0\cupΓ_1$ such that $\overline{Γ_0}\cap\overline{Γ_1}=\emptyset$. On $Γ_0$, we consider the homogeneous Dirichlet boundary condition, and on $Γ_1$ , we consider the acoustic boundary condition without a damping term. More precisely, by making use of semigroup techniques, well-posedness results are discussed, as well as the asymptotic behavior of solutions. The difficulty in establishing the stability of the system arises from the presence of higher-order operators, normal derivatives, and some boundary terms. The key tools combine the multiplier approach, trace theorems, ideas from Frota and Vicenté \cite{FrotaVicente2018}, and new technical arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of an elastodynamic system with localized internal damping and acoustic boundary conditions Balehouane, Abdelkhalek Kasri, Hicham Kechkar, Rokia Analysis of PDEs 93C20, 93D15, 93D23 In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $Ω$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to be locally distributed and satisfies suitable assumptions. The smooth boundary of $Ω$ is $Γ=Γ_0\cupΓ_1$ such that $\overline{Γ_0}\cap\overline{Γ_1}=\emptyset$. On $Γ_0$, we consider the homogeneous Dirichlet boundary condition, and on $Γ_1$ , we consider the acoustic boundary condition without a damping term. More precisely, by making use of semigroup techniques, well-posedness results are discussed, as well as the asymptotic behavior of solutions. The difficulty in establishing the stability of the system arises from the presence of higher-order operators, normal derivatives, and some boundary terms. The key tools combine the multiplier approach, trace theorems, ideas from Frota and Vicenté \cite{FrotaVicente2018}, and new technical arguments. |
| title | Stability of an elastodynamic system with localized internal damping and acoustic boundary conditions |
| topic | Analysis of PDEs 93C20, 93D15, 93D23 |
| url | https://arxiv.org/abs/2507.16546 |