Random attractors for a class of stochastic partial differential equations driven by general additive noise

Abstract

The existence of random attractors for a large class of stochastic partial differential equations (SPDE) driven by general additive noise is established. The main results are applied to various types of SPDE, as e.g. stochastic reaction-diffusion equations, the stochastic $p$-Laplace equation and stochastic porous media equations. Besides classical Brownian motion, we also include space-time fractional Brownian Motion and space-time Lévy noise as admissible random perturbations. Moreover, cases where the attractor consists of a single point are considered and bounds for the speed of attraction are obtained.

30 pages

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• Multi-valued, singular stochastic evolution inclusions
• Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
• Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts
• Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations
• Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise
• Singular Equations Driven by an Additive Noise and Applications
• Random attractor associated with the quasi-geostrophic equation
• Large deviation principle of occupation measures for Non-linear monotone SPDEs
• Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients
• Small Time Asymptotics for SPDEs with Locally Monotone Coefficients
• Ergodicity for singular-degenerate porous media equations
• LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter $H\in (1/4,1/2)$
• Random attractors for singular stochastic partial differential equations
• Weak Pullback Mean Random Attractors for Stochastic Evolution Equations and Applications
• Setvalued dynamical systems for stochastic evolution equations driven by fractional noise
• A random attractor for stochastic porous media equations on infinite lattices
• Finite speed of propagation for stochastic porous media equations
• Random Attractors for Stochastic Navier-Stokes equation on a 2D rotating sphere with stable Lévy noise
• On Young regimes for locally monotone SPDEs
• Synchronization, Lyapunov exponents and stable manifolds for random dynamical systems
• Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded Domains