\((L^2,H^1)\)-random attractors for stochastic reaction-diffusion equation on unbounded domains
Summary: We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space \(\mathbb R^n\) 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 \(p-1(p\geq 2)\). 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 \textit{B. Wang} [Physica D 128, No. 1, 41--52 (1999; Zbl 0953.35022)] and the cut-off technique.
scientific article; zbMATH DE number 6306595
scientific article