Random attractors for the stochastic Benjamin–Bona–Mahony equation on unbounded domains

Abstract: We prove the existence of a compact random attractor for the stochastic Benjamin–Bona–Mahony equation defined on an unbounded domain. This random attractor is invariant and attracts every pulled-back tempered random set under the forward flow. The asymptotic compactness of the random dynamical system is established by a tail-estimates method, which shows that the solutions are uniformly asymptotically small when space and time variables approach infinity. [Copyright &y& Elsevier]