论文标题
随机吸引子的上半频道和非局部随机Swift-Hohenberg方程的不变措施的存在
Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift-Hohenberg equation with multiplicative noise
论文作者
论文摘要
在本文中，我们主要研究2D非局域性随机Swift-Hohenberg方程的长期动力学行为，并从两个角度使用乘法噪声。首先，通过采用分析性半群理论，我们证明了sobolev空间中随机吸引子的上部半持续点$ h_0^2（u）$作为乘法噪声的系数接近零。然后，我们扩展了经典的“随机Gronwall的引理”，使其在应用中更加方便。基于这一改进，我们可以使用分析的半群理论来确定千古不变的措施的存在。
In this paper, we mainly study the long-time dynamical behaviors of 2D nonlocal stochastic Swift-Hohenberg equations with multiplicative noise from two perspectives. Firstly, by adopting the analytic semigroup theory, we prove the upper semi-continuity of random attractors in the Sobolev space $H_0^2(U)$, as the coefficient of the multiplicative noise approaches zero. Then, we extend the classical "stochastic Gronwall's lemma", making it more convenient in applications. Based on this improvement, we are allowed to use the analytic semigroup theory to establish the existence of ergodic invariant measures.
