Feedback boundary stabilization for the Hirota-Satsuma system with time-delay
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929553668046848 |
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| author | Martinez, Victor Hugo Gonzalez Muñoz, Juan Ricardo |
| author_facet | Martinez, Victor Hugo Gonzalez Muñoz, Juan Ricardo |
| contents | This work investigates the boundary stabilization problem of the Hirota-Satsuma system. In the problem under consideration, a boundary feedback law consisting of a linear combination of a damping mechanism and a time-delay term is designed. The study shows that, with time delay feedback and a smallness restriction on the size of the initial data the energy of the Hirota-Satsuma system decays exponentially by employing two approaches: the Lyapunov method and an observability inequality combined with a contradiction argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feedback boundary stabilization for the Hirota-Satsuma system with time-delay Martinez, Victor Hugo Gonzalez Muñoz, Juan Ricardo Analysis of PDEs 35Q53, 93D15, 93D30, 93C20 This work investigates the boundary stabilization problem of the Hirota-Satsuma system. In the problem under consideration, a boundary feedback law consisting of a linear combination of a damping mechanism and a time-delay term is designed. The study shows that, with time delay feedback and a smallness restriction on the size of the initial data the energy of the Hirota-Satsuma system decays exponentially by employing two approaches: the Lyapunov method and an observability inequality combined with a contradiction argument. |
| title | Feedback boundary stabilization for the Hirota-Satsuma system with time-delay |
| topic | Analysis of PDEs 35Q53, 93D15, 93D30, 93C20 |
| url | https://arxiv.org/abs/2408.15705 |