带有乘积白噪音的非自治随机波方程的随机吸引子

Random Attractors for Non-Autonomous Stochastic Wave Equation with Multiplicative Noise

研究了带有乘积白噪音的非自治随机波方程.首先证明解在一个有界球外的一致小性,然后对解在有界的区域内进行分解,得到解的渐近紧性,最后得到了带有乘积白噪音的非自治随机波方程的随机吸引子的存在性.

In this paper,we deal with the initial boundary value problem for non-autonomous stochastic wave equation with multiplicative noise,First,we prove the uniform miniaturity of the solution outside a bounded sphere.Then,we get the the asymptotic compactness of the solution by decomposing the solution in a bounded domain,Finally,the existence of random attractor for non-autonomous stochastic wave equation with multiplicative noise is obtained.