Fractal dimensions of random attractors for stochastic Benjamin–Bona–Mahony equation on unbounded domains☆

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Abstract

This paper considers random attractor and its fractal dimension for Benjamin–Bona–Mahony equation driven by additive white noise on unbounded domains . Firstly, we investigate the existence of random attractor for the random dynamical system defined on an unbounded domain. Secondly, we present criterion for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space. Finally, we apply expectations of some random variables and these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic Benjamin–Bona–Mahony equation driven by additive white noise.

Keywords

Fractal dimension
Random attractor
Unbounded domain
Stochastic Benjamin–Bona–Mahony equation

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This research is supported by Hunan Provincial Natural Science Foundation of China 2015JJ2144; partially supported by National Natural Science Foundation of People’s Republic of China under grant 11671343, 11171280, the General Project of the Education Department of Hunan Province under grant 12C0408.

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