Fractal dimension of random attractors for stochastic non-autonomous reaction–diffusion equations

摘要

In this paper, we first give some conditions for bounding the fractal dimension of a random invariant set for a non-autonomous random dynamical system on a separable Banach space. Then we apply these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic reaction–diffusion equations with multiplicative white noise and additive white noise.