A concept of a bi-spatial random attractor for a random dynamical system is introduced. A
unified result about existence and upper semi-continuity for a family of bi-spatial random …

The random dynamics in H s (Rn) with s∈(0, 1) is investigated for the fractional nonclassical
diffusion equations driven by colored noise. Both existence and uniqueness of pullback …

This paper first introduces the so-called quasi-continuous random dynamical system (RDS)
on a separable Banach space. The quasi-continuity is weaker than all the usual continuities …

A bi-spatial pullback attractor is obtained for non-autonomous and stochastic FitzHugh-
Nagumo equations when the initial space is $ L^ 2 (\mathbb {R}^ n)^ 2$ and the terminate …

We study in some detail the structure of the random attractor for the Chafee-Infante reaction-
diffusion equation perturbed by a multiplicative white noise, du=(Δ u+ β uu 3) dt+ σ uod W t …

In this paper we consider a class of a stochastic partial differential equations with
multiplicative noise and consider the limit of fast diffusion or other fast elliptic operator. We …

In the present work we consider a quite general class of reaction–diffusion equations forced
by additive and multiplicative noise. When the diffusion is large, one can approximate the …

In this paper, we first improve the existing conditions for the existence of a random
exponential attractor for a continuous cocycle on a separable Banach space. Then we …

We prove new L 2-estimates and regularity results for generalized porous media equations
“shifted by” a function-valued Wiener path. To include Wiener paths with merely first spatial …

Rigorous error estimates for amplitude equations are well known for deterministic PDEs, and
there is a large body of literature over the past two decades. However, there seems to be a …