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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| 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 |
| id | doaj-art-41bfb70198df4b5dae412692735ec651 |
| 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 |