(L2, H1)-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains. (21st December 2013) - Wang, Gang; Tang, Yanbin
Abstract : We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space ℝ n and prove the existence of an ( L 2, H 1 ) -random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy the growth of arbitrary order p - 1 (p ≥ 2 ). The ( L 2, H 1 ) -asymptotic compactness of the random dynamical system is obtained by using an extended version of the tail estimate method introduced by Wang (1999) and the cut-off technique.