On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise

DOI10.1142/S0219493718500405zbMath1403.37086OpenAlexW2769732428MaRDI QIDQ4687206

Jicheng Liu, Hongbo Fu, Xiang Jun Wang, Xian-Ming Liu

Publication date: 11 October 2018

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493718500405

zbMATH Keywords

stochastic partial differential equationsrandom dynamical systemsrandom attractorupper semi-continuityWong-Zakai approximation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) PDEs with randomness, stochastic partial differential equations (35R60) Infinite-dimensional random dynamical systems; stochastic equations (37L55)

Related Items

Wong–Zakai approximations of second-order stochastic lattice systems driven by additive white noise, High-order Wong-Zakai approximations for non-autonomous stochastic \(p\)-Laplacian equations on \(\mathbb{R}^N\), Regularity of Wong-Zakai approximation for stochastic reaction-diffusion equation on \(\mathbb{R}^N\), Higher-order Wong-Zakai approximations of stochastic reaction-diffusion equations on \(\mathbb{R}^N\), Wong-Zakai approximations and attractors for stochastic wave equations driven by additive noise, Wong–Zakai approximations of the non-autonomous stochastic FitzHugh–Nagumo system on RN in higher regular spaces

Cites Work

• Unnamed Item
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• Convergence rate of synchronization of systems with additive noise
• Random attractors for a class of stochastic partial differential equations driven by general additive noise
• Random attractor for stochastic reaction-diffusion equation with multiplicative noise on unbounded domains
• Approximation for random stable manifolds under multiplicative correlated noises
• Wong-Zakai approximations of stochastic evolution equations
• A Wong-Zakai theorem for stochastic PDEs
• Attractors for random dynamical systems
• Infinite-dimensional dynamical systems in mechanics and physics.
• Random attractors
• Smooth stable and unstable manifolds for stochastic evolutionary equations
• Stability of random attractors under perturbation and approximation
• Random attractors for stochastic reaction-diffusion equations on unbounded domains
• On the relation between ordinary and stochastic differential equations
• Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation
• Random Point Attractors Versus Random Set Attractors
• An approach to Ito linear equations in Hilbert spaces by approximation of white noise with coloured noise
• Upper Semicontinuity of Random Attractors for Non-compact Random Dynamical Systems
• Attractors for non-compact semigroups via energy equations
• Upper semicontinuity of attractors for small random perturbations of dynamical systems
• Random attractors of stochastic partial differential equations: A smooth approximation approach
• On the Convergence of Ordinary Integrals to Stochastic Integrals