(L2, H1)-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains. (21st December 2013)

• Record Type: Journal Article
• Authors: Wang, Gang; Tang, Yanbin
• Other Names: Lukaszewicz Grzegorz Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-12-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/279509
• Languages: English
• ISSNs: 1085-3375

Abstract

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.