Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition

We consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then...

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Main Authors: Na Liu, Jie Xin
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/3642548
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author Na Liu
Jie Xin
author_facet Na Liu
Jie Xin
author_sort Na Liu
collection DOAJ
description We consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then a global random attractor and the existence of a stationary measure are obtained via the Birkhoff ergodic theorem and the Chebyshev inequality.
format Article
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institution OA Journals
issn 1026-0226
1607-887X
language English
publishDate 2017-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-41bfb70198df4b5dae412692735ec6512025-08-20T02:08:26ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/36425483642548Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary ConditionNa Liu0Jie Xin1School of Mathematics and Statistics Science, Ludong University, Yantai City 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai City 264025, ChinaWe consider the asymptotic behaviors of stochastic fractional long-short equations driven by a random force. Under a priori estimates in the sense of expectation, using Galerkin approximation by the stopping time and the Borel-Cantelli lemma, we prove the existence and uniqueness of solutions. Then a global random attractor and the existence of a stationary measure are obtained via the Birkhoff ergodic theorem and the Chebyshev inequality.http://dx.doi.org/10.1155/2017/3642548
spellingShingle Na Liu
Jie Xin
Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
Discrete Dynamics in Nature and Society
title Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
title_full Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
title_fullStr Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
title_full_unstemmed Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
title_short Existence of Random Attractor for Stochastic Fractional Long-Short Wave Equations with Periodic Boundary Condition
title_sort existence of random attractor for stochastic fractional long short wave equations with periodic boundary condition
url http://dx.doi.org/10.1155/2017/3642548
work_keys_str_mv AT naliu existenceofrandomattractorforstochasticfractionallongshortwaveequationswithperiodicboundarycondition
AT jiexin existenceofrandomattractorforstochasticfractionallongshortwaveequationswithperiodicboundarycondition