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

Yanfeng Guo
2015 Journal of Inequalities and Applications  
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
more » ... nifold 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. MSC: 60H15; 76A05; 37H05; 37L55
doi:10.1186/s13660-015-0889-8 fatcat:z6w576xvufdllforg6ftggbyt4