数学
遍历理论
半群
乘性噪声
吸引子
不变测度
不变(物理)
数学分析
乘法函数
随机动力系统
纯数学
应用数学
数学物理
电气工程
信号传递函数
工程类
线性系统
线性动力系统
数字信号处理
模拟信号
作者
Jintao Wang,Chunqiu Li,Lu Yang,Man Jia
摘要
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.
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