This paper deals with the limiting behavior of random attractors of stochastic wave equations with supercritical drift driven by linear multiplicative white noise defined on unbounded domains. We first establish the uniform Strichartz estimates of the solutions with respect to noise intensity, and then prove the convergence of the solutions of the stochastic equations with respect to initial data as well as noise intensity. To overcome the non-compactness of Sobolev embeddings on unbounded domains, we first utilize the uniform tail-ends estimates to truncate the solutions in a bounded domain and then employ a spectral decomposition to establish the pre-compactness of the collection of all random attractors. We finally prove the upper semicontinuity of random attractor as noise intensity approaches zero.

本文研究了由无界域上定义的线性乘性白噪声驱动的具有超临界漂移的随机波动方程的随机吸引子的极限行为。我们首先建立关于噪声强度的解的均匀 Strichartz 估计，然后证明随机方程的解对于初始数据和噪声强度的收敛性。为了克服无界域上 Sobolev 嵌入的非紧性，我们首先利用统一尾端估计来截断有界域中的解，然后采用谱分解来建立所有随机吸引子集合的预紧性。我们最终证明了当噪声强度接近零时随机吸引子的上半连续性。