Czechoslovak Mathematical Journal, first online, pp. 1-23
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
Received March 28, 2019. Published online August 18, 2020.
Abstract: We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space $\Rd$ driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted $L^2$-space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Keywords: reaction-diffusion equation; random attractor; spatially homogeneous noise