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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.04481 |
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Table of 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.