Mixing for acoustic wave motion with boundary random force
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866918059482021888 |
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| author | Jiao, Zhe Li, Xiao |
| author_facet | Jiao, Zhe Li, Xiao |
| contents | This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup generated by a stochastic evolution equation and the observability property of the corresponding adjoint system. This result is then applied to study the mixing for acoustic wave system with a boundary random perturbation of the white noise type. We shall show there exists a unique invariant measure for the stochastic wave system, and the law of the solution to the system converges to this invariant measure weakly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_04481 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mixing for acoustic wave motion with boundary random force Jiao, Zhe Li, Xiao Analysis of PDEs This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup generated by a stochastic evolution equation and the observability property of the corresponding adjoint system. This result is then applied to study the mixing for acoustic wave system with a boundary random perturbation of the white noise type. We shall show there exists a unique invariant measure for the stochastic wave system, and the law of the solution to the system converges to this invariant measure weakly. |
| title | Mixing for acoustic wave motion with boundary random force |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2203.04481 |