Local large deviations for randomly forced nonlinear wave equations with localized damping
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912033541193728 |
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| author | Chen, Yuxuan Liu, Ziyu Xiang, Shengquan Zhang, Zhifei |
| author_facet | Chen, Yuxuan Liu, Ziyu Xiang, Shengquan Zhang, Zhifei |
| contents | We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a local type. The primary challenge is the lack of compactness due to the absence of smoothing effect. This is overcome by exploiting the asymptotic compactness for the dynamics of waves, introducing the concept of asymptotic exponential tightness for random measures, and establishing a new LDP approach for random dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local large deviations for randomly forced nonlinear wave equations with localized damping Chen, Yuxuan Liu, Ziyu Xiang, Shengquan Zhang, Zhifei Analysis of PDEs Optimization and Control Probability 37L50, 35L71, 60B12, 60F10 We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a local type. The primary challenge is the lack of compactness due to the absence of smoothing effect. This is overcome by exploiting the asymptotic compactness for the dynamics of waves, introducing the concept of asymptotic exponential tightness for random measures, and establishing a new LDP approach for random dynamical systems. |
| title | Local large deviations for randomly forced nonlinear wave equations with localized damping |
| topic | Analysis of PDEs Optimization and Control Probability 37L50, 35L71, 60B12, 60F10 |
| url | https://arxiv.org/abs/2409.11717 |