Dynamics and invariant manifolds for a nonlocal stochastic Swift-Hohenberg equation

作者：Guo; Yanfeng

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015, 2015(1): 366.

DOI：10.1186/s13660-015-0889-8

• nonlocal stochastic Swift-Hohenberg equation
• stochastic transformation
• cut-off function
• random attractor
• invariant manifolds

The dynamics and invariant manifolds for a nonlocal stochastic Swift-Hohenberg equation with multiplicative noise are investigated. Using a stochastic transformation process, a nonlocal stochastic Swift-Hohenberg equation is studied with either a positive kernel or a non-negative kernel. Then the dynamics, existence, and uniqueness of a global random attractor for the nonlocal stochastic Swift-Hohenberg equation is shown. Moreover, the existence of a local random invariant manifold of the corresponding random dynamical system for the nonlocal stochastic Swift-Hohenberg equation with multiplicative noise is obtained using the technique of a cut-off function and the Lyapunov-Perron method.

• 出版日期2015-11-21
• 单位广西大学