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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25484 |
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| _version_ | 1866908841907585024 |
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| author | Siriki, Ben Bakary Junior Coulibaly, Adama |
| author_facet | Siriki, Ben Bakary Junior Coulibaly, Adama |
| contents | This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an appropriate energy space in weighted Sobolev settings. Using Lümer-Phillips theorem, we prove that the linear operator associated with the problem generates a $\mathcal{C}_0$-semigroup of contractions. Next, we establish the uniform exponential stability of the system. By constructing a novel Lyapunov functional incorporating weighted integral terms, we demonstrate that the energy of the system exponentially decays to zero and derive a precise decay rate estimate. This work provides a significant extension to the stability theory for complex distributed parameter systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Stability of a Degenerate Euler-Bernoulli Beam with Axial Force and Delayed Boundary Control Siriki, Ben Bakary Junior Coulibaly, Adama Analysis of PDEs This work investigates the global exponential stabilization of a degenerate Euler-Bernoulli beam subjected to a non uniform axial force and a delayed feedback control. First, we address the well-posedness of the system by constructing an appropriate energy space in weighted Sobolev settings. Using Lümer-Phillips theorem, we prove that the linear operator associated with the problem generates a $\mathcal{C}_0$-semigroup of contractions. Next, we establish the uniform exponential stability of the system. By constructing a novel Lyapunov functional incorporating weighted integral terms, we demonstrate that the energy of the system exponentially decays to zero and derive a precise decay rate estimate. This work provides a significant extension to the stability theory for complex distributed parameter systems. |
| title | Exponential Stability of a Degenerate Euler-Bernoulli Beam with Axial Force and Delayed Boundary Control |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.25484 |