This paper mainly investigates the asymptotic behavior of non-autonomous stochastic complex Ginzburg–Landau equations on unbounded thin domains. We first prove the existence and uniqueness of random attractors for the considered equation and its limit equation. Due to the non-compactness of Sobolev embeddings on unbounded domains, the pullback asymptotic compactness of such a stochastic equation is proved by the tail-estimate method. Then, we show the upper semi-continuity of random attractors when thin domains collapse onto the real space $\mathbb{R}$.

中文翻译：

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无界薄域上非自治随机复Ginzburg-Landau方程的渐近行为

本文主要研究非自治随机复Ginzburg-Landau方程在无界薄域上的渐近行为。我们首先证明了所考虑方程及其极限方程的随机吸引子的存在性和唯一性。由于Sobolev嵌入在无界域上的非紧致性，因此通过尾部估计方法证明了这种随机方程的拉回渐近紧致性。然后，我们显示了当薄域塌陷到真实空间时随机吸引子的上半连续性$\mathbb{[R}$。