Communications in Mathematical Sciences

Volume 13 (2015)

Number 2

Random attractor and stationary measure for stochastic long-short wave equations

Pages: 539 – 555

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n2.a14

Authors

Donglong Li (School of Science, Guangxi University of Science and Technology, Guangxi, China)

Yanfeng Guo (School of Science, Guangxi University of Science and Technology, Guangxi, China; and Institute of Applied Physics and Computational Mathematics, Beijing, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Abstract

Asymptotic behaviors of stochastic long-short equations driven by a random force, which is smooth enough in space and white noise in time, are mainly considered. The existence and uniqueness of solutions for stochastic long-short equations are obtained via Galerkin approximation by the stopping time and the Borel-Cantelli Lemma on the basis of a priori estimates in the sense of expectation. A global random attractor and the existence of a stationary measure are investigated by the Birkhoff ergodic theorem and the Chebyshev inequality.

Keywords

stochastic long-short equations, existence and uniqueness, global random attractor, stationary measure

2010 Mathematics Subject Classification

35Q35, 60H15, 76B03

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Published 3 December 2014