Smooth stable and unstable manifolds for stochastic evolutionary equations
From MaRDI portal
Publication:1763018
DOI10.1007/s10884-004-7830-zzbMath1065.60077arXivmath/0409483OpenAlexW3103931584MaRDI QIDQ1763018
Kening Lu, Björn Schmalfuss, Jin-qiao Duan
Publication date: 18 February 2005
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0409483
Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Invariant manifold theory for dynamical systems (37D10) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25) Infinite-dimensional random dynamical systems; stochastic equations (37L55)
Related Items (90)
Unstable manifolds for rough evolution equations ⋮ Center manifolds for ill-posed stochastic evolution equations ⋮ Limiting behavior of center manifolds for stochastic evolutionary equations with delay in varying phase spaces ⋮ APPROXIMATION OF INVARIANT FOLIATIONS FOR STOCHASTIC DYNAMICAL SYSTEMS ⋮ Approximation of random slow manifolds and settling of inertial particles under uncertainty ⋮ Unstable manifolds for rough evolution equations ⋮ INVARIANT MANIFOLDS FOR STOCHASTIC MODELS IN FLUID DYNAMICS ⋮ Slow manifold and parameter estimation for a nonlocal fast-slow dynamical system with Brownian motion ⋮ On growth rates of sub-additive functions for semi-flows: determined and random cases ⋮ Centre manifolds for stochastic evolution equations ⋮ Global synchronising behavior of evolution equations with exponentially growing nonautonomous forcing ⋮ Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms ⋮ Nonuniform \((h,k,\mu,\nu)\)-dichotomy with applications to nonautonomous dynamical systems ⋮ Approximate the dynamical behavior for stochastic systems by Wong-zakai approaching ⋮ On the Oseledets-splitting for infinite-dimensional random dynamical systems ⋮ Multivalued perturbations of a saddle dynamics ⋮ Invariant manifolds for stochastic wave equations ⋮ Smooth convergence of random center manifolds for SPDEs in varying phase spaces ⋮ Singular limit of mean-square invariant unstable manifolds for SPDEs driven by nonlinear multiplicative white noise in varying phase spaces ⋮ Qualitative properties of local random invariant manifolds for SPDEs with quadratic nonlinearity ⋮ Computational singular perturbation analysis of stochastic chemical systems with stiffness ⋮ Conjugate dynamics on center-manifolds for stochastic partial differential equations ⋮ Mean-square invariant manifolds for stochastic weak-damping wave equations with nonlinear noise ⋮ Forward dynamics and memory effect in a fractional order chemostat minimal model with non-monotonic growth ⋮ Synchronization of stochastic lattice equations ⋮ Pathwise unstable invariant manifolds reduction for stochastic evolution equations driven by nonlinear noise ⋮ Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain ⋮ Effective filtering for slow-fast systems via Wong-Zakai approximation ⋮ Invariant manifolds and foliations for random differential equations driven by colored noise ⋮ A Wong-Zakai approximation for random invariant manifolds ⋮ Center manifolds for rough partial differential equations ⋮ Stability and constructions of the Poincaré maps for a class of stochastic partial differential equations ⋮ Smoothness of invariant manifolds and foliations for infinite dimensional random dynamical systems ⋮ Existence of smooth stable manifolds for a class of parabolic SPDEs with fractional noise ⋮ The Burgers equation with affine linear noise: dynamics and stability ⋮ Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding ⋮ Persistence of smooth manifolds for a non-autonomous coupled system under small random perturbations ⋮ Moment boundedness of linear stochastic delay differential equations with distributed delay ⋮ Approximations of center manifolds for delay stochastic differential equations with additive noise ⋮ \(L^{p}\) (\(p\geq 2\))-strong convergence in averaging principle for multivalued stochastic differential equation with non-Lipschitz coefficients ⋮ Slow foliation of a slow-fast stochastic evolutionary system ⋮ Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations ⋮ The Wong-Zakai approximations of invariant manifolds and foliations for stochastic evolution equations ⋮ A dynamical approximation for stochastic partial differential equations ⋮ Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients ⋮ Second moment boundedness of linear stochastic delay differential equations ⋮ INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ Invariant manifolds for nonautonomous stochastic evolution equation ⋮ Smooth invariant manifolds for a randomly perturbed non-autonomous coupled system and their approximations ⋮ Stationary solutions of SPDEs and infinite horizon BDSDEs ⋮ Climate dynamics and fluid mechanics: Natural variability and related uncertainties ⋮ An averaging principle for McKean-Vlasov-type Caputo fractional stochastic differential equations ⋮ Mean-square random invariant manifolds for stochastic differential equations ⋮ Strong approximation rate for Wiener process by fast oscillating integrated Ornstein-Uhlenbeck processes ⋮ Unstable invariant manifolds for stochastic PDEs driven by a fractional Brownian motion ⋮ Approximation of the random inertial manifold of singularly perturbed stochastic wave equations ⋮ STOCHASTIC INERTIAL MANIFOLDS FOR DAMPED WAVE EQUATIONS ⋮ Pathwise random periodic solutions of stochastic differential equations ⋮ Dynamics of stochastic 2D Navier-Stokes equations ⋮ Centre manifolds for infinite dimensional random dynamical systems ⋮ Slow manifold for a nonlocal stochastic evolutionary system with fast and slow components ⋮ Wong-Zakai approximations and center manifolds of stochastic differential equations ⋮ On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise ⋮ Approximation for random stable manifolds under multiplicative correlated noises ⋮ Approximation of random invariant manifolds for a stochastic Swift-Hohenberg equation ⋮ A dynamical theory for singular stochastic delay differential equations. II: Nonlinear equations and invariant manifolds ⋮ Existence-uniqueness and stability of the mild periodic solutions to a class of delayed stochastic partial differential equations and its applications ⋮ Periodic and Almost Periodic Random Inertial Manifolds for Non-Autonomous Stochastic Equations ⋮ A Wong-Zakai approximation for random slow manifolds with application to parameter estimation ⋮ Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise ⋮ Finite dimensional reducing and smooth approximating for a class of stochastic partial differential equations ⋮ Limiting behavior of unstable manifolds for SPDEs in varying phase spaces ⋮ Random invariant manifolds for ill-posed stochastic evolution equations ⋮ Representation of manifolds for the stochastic Swift-Hohenberg equation with multiplicative noise ⋮ \(C^{1, \nu }\)-convergence of center manifolds for stochastic PDEs driven by colored noise on thin domain ⋮ Approximate dynamics of a class of stochastic wave equations with white noise ⋮ Slow manifolds for a nonlocal fast-slow stochastic system with stable Lévy noise ⋮ REPRESENTATION OF PATHWISE STATIONARY SOLUTIONS OF STOCHASTIC BURGERS' EQUATIONS ⋮ Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise ⋮ Normally hyperbolic invariant manifolds for random dynamical systems: Part I - persistence ⋮ An impact of noise on invariant manifolds in nonlinear dynamical systems ⋮ Rough Center Manifolds ⋮ Master-slave synchronization and invariant manifolds for coupled stochastic systems ⋮ Effective approximation of stochastic sine-Gordon equation with a fast oscillation ⋮ Random invariant manifolds of stochastic evolution equations driven by Gaussian and non-Gaussian noises ⋮ Invariant foliations for stochastic partial differential equations with non-dense domain ⋮ The Poincaré maps of a slow-fast stochastic system ⋮ Geometric shape of invariant manifolds for a class of stochastic partial differential equations ⋮ Transitions in stochastic non-equilibrium systems: efficient reduction and analysis ⋮ Invariant foliations for stochastic partial differential equations with dynamic boundary conditions
Cites Work
- Characteristic exponents and invariant manifolds in Hilbert space
- Smooth invariant foliations in infinite dimensional spaces
- A random fixed point theorem and the random graph transformation
- The random attractor of the stochastic Lorenz system
- Exponentially stable stationary solutions for stochastic evolution equations and their perturba\-tion
- The stable manifold theorem for stochastic differential equations
- Existence and persistence of invariant manifolds for semiflows in Banach space
- A stochastic pitchfork bifurcation in a reaction-diffusion equation
- Inertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systems
This page was built for publication: Smooth stable and unstable manifolds for stochastic evolutionary equations
