Centre manifolds for stochastic evolution equations

DOI10.1080/10236198.2015.1045889zbMath1325.60103arXiv1210.5924OpenAlexW2092076989MaRDI QIDQ3195513

Xiao-Peng Chen, Jin-qiao Duan, Anthony Roberts

Publication date: 20 October 2015

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.5924

zbMATH Keywords

stabilitystochastic partial differential equationsexponential trichotomycentre manifoldsdynamical approximation

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Invariant manifold theory for dynamical systems (37D10) Stability of manifolds of solutions to ordinary differential equations (34D35)

Related Items

Unstable manifolds for rough evolution equations, Center manifolds for ill-posed stochastic evolution equations, Unstable manifolds for rough evolution equations, Convergence of Equation-Free Methods in the Case of Finite Time Scale Separation with Application to Deterministic and Stochastic Systems, On the Oseledets-splitting for infinite-dimensional random dynamical systems, Center manifolds for rough partial differential equations, Centre manifolds for infinite dimensional random dynamical systems, A dynamical theory for singular stochastic delay differential equations. II: Nonlinear equations and invariant manifolds, Random invariant manifolds for ill-posed stochastic evolution equations, Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise, Rough Center Manifolds, Invariant foliations for stochastic partial differential equations with non-dense domain

Cites Work

• Unnamed Item
• Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
• Center manifolds and contractions on a scale of Banach spaces
• A stochastic version of center manifold theory
• On nonlinear problems of mixed type: A qualitative theory using infinite- dimensional center manifolds
• Smoothness of inertial manifolds
• Existence of dichotomies and invariant splittings for linear differential systems. III
• Low-dimensional modelling of dynamics via computer algebra
• Robustness of exponential dichotomies in infinite-dimensional dynamical systems
• Center manifolds for infinite dimensional nonautonomous differential equations
• Invariant manifolds for stochastic partial differential equations.
• Smooth stable and unstable manifolds for stochastic evolutionary equations
• Exponentially stable stationary solutions for stochastic evolution equations and their perturba\-tion
• A center-stable manifold theorem for differential equations in Banach spaces
• The stable manifold theorem for stochastic differential equations
• On the stability of the center manifold
• Smooth center manifolds for nonuniformly partially hyperbolic trajectories
• Resolving the Multitude of Microscale Interactions Accurately Models Stochastic Partial Differential Equations
• A dynamical approximation for stochastic partial differential equations
• Model Dynamics across Multiple Length and Time Scales on a Spatial Multigrid
• On the Spectrum of C 0 -Semigroups
• The application of centre-manifold theory to the evolution of system which vary slowly in space
• Boundary conditions for approximate differential equations
• Construction of stochastic inertial manifolds using backward integration
• A stochastic pitchfork bifurcation in a reaction-diffusion equation
• Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations
• Stochastic inertial manifold
• An impact of noise on invariant manifolds in nonlinear dynamical systems
• Geometric shape of invariant manifolds for a class of stochastic partial differential equations