One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913763945349120 |
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| author | Dahmani, Abdelhakim Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe |
| author_facet | Dahmani, Abdelhakim Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe |
| contents | This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish the exponential decay of solutions towards the corresponding steady states. The results are obtained either by the multiplier method or spectral analysis in an $L^2$-functional framework, and then with input-to-state technics in an $L^p$-functional framework for $p \in (2,\infty)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_22439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions Dahmani, Abdelhakim Chitour, Yacine Nguyen, Hoai-Minh Roman, Christophe Analysis of PDEs Optimization and Control 35L05, 93D23, 93D15 This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish the exponential decay of solutions towards the corresponding steady states. The results are obtained either by the multiplier method or spectral analysis in an $L^2$-functional framework, and then with input-to-state technics in an $L^p$-functional framework for $p \in (2,\infty)$. |
| title | One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions |
| topic | Analysis of PDEs Optimization and Control 35L05, 93D23, 93D15 |
| url | https://arxiv.org/abs/2503.22439 |