Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains

Details Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains Random Attractors for the Stochastic Benjamin-Bona-Mahony Equation on Unbounded Domains

2008-05-13

arxiv.org/abs/0805.1781v1

Mathematics

Analysis of PDEs

37 pages

Scientific paper

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.

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