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

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

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 frac...

Stochastic Partial Differential Equations Driven by Purely Spatial Noise

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron–Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

8 Stochastic Partial Differential Equations Driven by Purely Spatial Noise

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

Attractors for Stochastic Strongly Damped Plate Equations with Additive Noise

We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.

The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise