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Dynamics and invariant manifolds for a nonlocal stochastic Swift-Hohenberg equation
- Source :
- Journal of Inequalities and Applications. 2015(1)
- Publisher :
- Springer Nature
-
Abstract
- 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.
- Subjects :
- Stochastic control
Astrophysics::High Energy Astrophysical Phenomena
Applied Mathematics
Invariant manifold
Mathematical analysis
Multiplicative noise
Swift–Hohenberg equation
Stochastic differential equation
Attractor
Applied mathematics
Discrete Mathematics and Combinatorics
Invariant (mathematics)
Random dynamical system
Nonlinear Sciences::Pattern Formation and Solitons
Analysis
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 1029242X
- Volume :
- 2015
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Inequalities and Applications
- Accession number :
- edsair.doi.dedup.....cac79e68f3f757fb5724a998f605f7d9
- Full Text :
- https://doi.org/10.1186/s13660-015-0889-8