Polynomial Stability of an Elastic Thin Plate on Non-Smooth Domain
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915919933997056 |
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| author | Sun, Ya-nan Zhang, Qiong |
| author_facet | Sun, Ya-nan Zhang, Qiong |
| contents | This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem as a precise variational framework. We prove that for domains with sufficiently small corner angles, the system retains the polynomial decay rate under standard geometric control conditions. In cases where larger corner angles lead to a significant regularity loss, we show that polynomial stability is recovered by introducing a feedback control at the corners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05401 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial Stability of an Elastic Thin Plate on Non-Smooth Domain Sun, Ya-nan Zhang, Qiong Analysis of PDEs 35B35, 93D20, 35Q74, 47D06 G.1.8 This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem as a precise variational framework. We prove that for domains with sufficiently small corner angles, the system retains the polynomial decay rate under standard geometric control conditions. In cases where larger corner angles lead to a significant regularity loss, we show that polynomial stability is recovered by introducing a feedback control at the corners. |
| title | Polynomial Stability of an Elastic Thin Plate on Non-Smooth Domain |
| topic | Analysis of PDEs 35B35, 93D20, 35Q74, 47D06 G.1.8 |
| url | https://arxiv.org/abs/2604.05401 |