带边界随机力的声波运动的混合性
Mixing for acoustic wave motion with boundary random force
AI总结：
本文建立随机演化方程马尔可夫半群正则性与伴随系统能观性的关联，证明带白噪声边界随机扰动的声波系统存在唯一不变测度且解的分布弱收敛于该测度，揭示其大时间混合行为。
摘要：
本文研究由边界作用的随机力驱动的声波运动的大时间行为。我们首先给出一个抽象结果，表明随机演化方程生成的马尔可夫半群的正则性与对应伴随系统的能观性之间存在关联。随后将该结果应用于研究带白噪声型边界随机扰动的声波系统的混合性。我们将证明该随机波动系统存在唯一不变测度，且系统解的概率分布弱收敛于该不变测度。
英文摘要：
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.
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