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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.02628 |
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| _version_ | 1866913786725662720 |
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| author | Chen, Bochao Gao, Yixian Feng, Zhaosheng Liu, Huiying |
| author_facet | Chen, Bochao Gao, Yixian Feng, Zhaosheng Liu, Huiying |
| contents | Response solutions are quasi-periodic ones with the same frequency as the forcing term. The present work is devoted to constructing response solutions for $d$-dimensional nonlinear plate models with nonlocal energy
damping, which are closely related to damping phenomena in flight structures.
For such models, the main characteristic is that the dissipation rate depends on the energy strength. By considering a small parameter $ε$ in the domain excluding the origin and imposing a small quasi-periodic forcing with a Diophantine frequency vector, we demonstrate the persistence of the corresponding response solution. We provide an alternative approach to the contraction mapping principle (cf. [7, 33]) through a combination of reduction together with the Nash--Moser iteration technique. The reason behind this approach lies in the derivative losses caused by the nonlocal nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-periodic response solutions of nonlinear plate models with nonlocal energy damping Chen, Bochao Gao, Yixian Feng, Zhaosheng Liu, Huiying Analysis of PDEs Dynamical Systems 37K55, 35Q40 G.0 Response solutions are quasi-periodic ones with the same frequency as the forcing term. The present work is devoted to constructing response solutions for $d$-dimensional nonlinear plate models with nonlocal energy damping, which are closely related to damping phenomena in flight structures. For such models, the main characteristic is that the dissipation rate depends on the energy strength. By considering a small parameter $ε$ in the domain excluding the origin and imposing a small quasi-periodic forcing with a Diophantine frequency vector, we demonstrate the persistence of the corresponding response solution. We provide an alternative approach to the contraction mapping principle (cf. [7, 33]) through a combination of reduction together with the Nash--Moser iteration technique. The reason behind this approach lies in the derivative losses caused by the nonlocal nonlinearity. |
| title | Quasi-periodic response solutions of nonlinear plate models with nonlocal energy damping |
| topic | Analysis of PDEs Dynamical Systems 37K55, 35Q40 G.0 |
| url | https://arxiv.org/abs/2401.02628 |