Slow manifold for a nonlocal stochastic evolutionary system with fast and slow components

DOI10.1016/j.jde.2017.06.003zbMath1432.35218OpenAlexW2647489292MaRDI QIDQ2013917

Lu Bai, Xiujun Cheng, Mei-Hua Yang, Jin-qiao Duan

Publication date: 10 August 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.06.003

zbMATH Keywords

reduced systemrandom dynamical systemsnonlocal Laplacian operatorrandom invariant manifoldsslow manifolds

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Generation, random and stochastic difference and differential equations (37H10) PDEs with randomness, stochastic partial differential equations (35R60) Fractional partial differential equations (35R11)

Related Items

Slow manifold and parameter estimation for a nonlocal fast-slow dynamical system with Brownian motion, Effective reduction for a nonlocal Zakai stochastic partial differential equation in data assimilation, Effective filtering for slow-fast systems via Wong-Zakai approximation, Slow manifolds for a nonlocal fast-slow stochastic system with stable Lévy noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximation of random slow manifolds and settling of inertial particles under uncertainty
• A nonlocal Fokker-Planck equation for non-Gaussian stochastic dynamical systems
• Slow manifolds for multi-time-scale stochastic evolutionary systems
• Invariant manifolds for flows in Banach spaces
• Slow manifold and averaging for slow-fast stochastic differential system
• Eigenvalues of the fractional Laplace operator in the interval
• Variational problems with free boundaries for the fractional Laplacian
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• Smooth invariant foliations in infinite dimensional spaces
• Convex analysis and measurable multifunctions
• A random fixed point theorem and the random graph transformation
• Center manifolds for infinite dimensional nonautonomous differential equations
• Invariant manifolds for stochastic partial differential equations.
• The Hartman-Grobman theorem for Carathéodory-type differential equations in Banach spaces
• Smooth stable and unstable manifolds for stochastic evolutionary equations
• Exponentially stable stationary solutions for stochastic evolution equations and their perturba\-tion
• Approximate inertial manifolds of exponential order for semilinear parabolic equations subjected to additive white noise
• Invariant manifolds for random dynamical systems with slow and fast variables
• Simulating Stochastic Inertial Manifolds by a Backward-Forward Approach
• APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS
• INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• Lévy Processes and Stochastic Calculus
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations
• An Introduction to Partial Differential Equations
• Stochastic inertial manifold
• Master-slave synchronization and invariant manifolds for coupled stochastic systems
• The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations
• Probleme General de la Stabilite du Mouvement. (AM-17)
• Dynamics of evolutionary equations
• Stochastic Equations in Infinite Dimensions