Abstract This paper deals with the limiting behavior of non-autonomous stochastic reaction-diffusion equations without uniqueness on unbounded narrow domains. We prove the existence and upper semicontinuity of random attractors for the equations on a family of unbounded (n + 1)-dimensional narrow domains, which collapses onto an n-dimensional domain. Since the solutions are non-uniqueness, which leads to a multivalued random dynamical system with the solution operators of the equation, we will prove the existence and upper semicontinuity of attractors by multivalued random dynamical system theory.

中文翻译：

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无界窄域上无唯一性的非自治随机演化方程的随机动力学

摘要 本文研究了无界窄域上无唯一性的非自治随机反应扩散方程的极限行为。我们证明了一系列无界 (n + 1) 维窄域上的方程的随机吸引子的存在性和上半连续性，这些域折叠到一个 n 维域上。由于解是非唯一性的，导致方程的解算符为多值随机动力系统，我们将用多值随机动力系统理论证明吸引子的存在性和上半连续性。