论文标题
混合声波运动与边界随机力
Mixing for acoustic wave motion with boundary random force
论文作者
论文摘要
本文关注的是由通过边界作用的随机力驱动的声波运动的较大时间行为。我们从一个抽象的结果开始，显示由随机演化方程生成的马尔可夫半群的规律性与相应伴随系统的可观察性属性之间的互连。然后将此结果应用于与白噪声类型的边界随机扰动一起进行声波系统的混合。我们将表明，存在一个独特的随机波系统的不变度，而对系统的解决方案的定律会收敛到这种不变的度量。
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.
