具时空白噪声1阶双曲系统的稳定性分析

Stability analysis for first-order hyperbolic systems with space-time white noise

对具有时空白噪声的1阶双曲系统的稳定性进行了分析.首先,利用Fourier变换将系统转化成一般抽象形式的随机演化方程,然后利用随机分析的方法给出了系统的均方指数稳定和几乎必然指数稳定的充分条件,最后给出实例说明方法的有效性.

The stability of first-order hyperbolic system with space-time white noise is discussed.The system is transformed into an abstract stochastic evolution equation using Fourier transformation;sufficient conditions are given for exponentially stable in mean-square and exponentially stable in almost sure.An example is provided to illustrate our theory.