The lack of exponential stability of a Bresse system subjected only to two dampings
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914638713585664 |
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| author | Régnier, Virginie Youssef, Waël |
| author_facet | Régnier, Virginie Youssef, Waël |
| contents | In this paper, we study the indirect boundary stabilization of a Bresse system with only two dissipation laws. This system, which models the dynamics of a beam, is a hyperbolic system with three wave speeds. We study the asymptotic behaviour of the eigenvalues and of the eigenvectors of the underlying operator in the case of three distinct wave velocities which is not physically relevant. Since the imaginary axis is proved to be an asymptote for one family of eigenvalues, the stability can not be exponential. Of course, this paper is only interesting from a mathematical point of view. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The lack of exponential stability of a Bresse system subjected only to two dampings Régnier, Virginie Youssef, Waël Analysis of PDEs 74K10, 35B40, 35Q74, 35B35, 35E15, 34L10, 34L15, 34L20, 93D15 In this paper, we study the indirect boundary stabilization of a Bresse system with only two dissipation laws. This system, which models the dynamics of a beam, is a hyperbolic system with three wave speeds. We study the asymptotic behaviour of the eigenvalues and of the eigenvectors of the underlying operator in the case of three distinct wave velocities which is not physically relevant. Since the imaginary axis is proved to be an asymptote for one family of eigenvalues, the stability can not be exponential. Of course, this paper is only interesting from a mathematical point of view. |
| title | The lack of exponential stability of a Bresse system subjected only to two dampings |
| topic | Analysis of PDEs 74K10, 35B40, 35Q74, 35B35, 35E15, 34L10, 34L15, 34L20, 93D15 |
| url | https://arxiv.org/abs/2307.11501 |