Dynamic behaviors of a local modified stochastic Swift-Hohenberg equation with multiplicative noise

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• 作者：Chunxiao Guo ; Yanfeng Guo ; Chengyuan Li
• 关键词：local modified stochastic Swift ; Hohenberg equation ; uniform a priori estimates ; random attractor
• 刊名：Boundary Value Problems
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1560KB
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770
• 卷排序：2017

文摘

In this paper, we investigate a global random attractor for a stochastic local modified Swift-Hohenberg equation with multiplicative noise in Stratonovich sense. Through the Ornstein-Uhlenbeck (O-U) transformation, we obtain the random dynamical system associated with the stochastic local modified Swift-Hohenberg equation. Using the properties of the O-U process, we derive the specific uniform a priori estimates, using which we prove the existence of global random attractor for the corresponding random dynamical system.