Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain
Abstract In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings. Then, we consider the stochastic Swift-Hohenber...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1166-1 |
| _version_ | 1818273428246888448 |
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| author | CX Guo YY Chen YF Guo |
| author_facet | CX Guo YY Chen YF Guo |
| author_sort | CX Guo |
| collection | DOAJ |
| description | Abstract In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings. Then, we consider the stochastic Swift-Hohenberg equation driven by additive noise on an unbounded domain and prove that the random dynamical system is asymptotically compact by uniform a priori estimates for the far-field values of the solution, which implies the existence of a random attractor for the random dynamical system associated with the stochastic Swift-Hohenberg equation. |
| first_indexed | 2024-12-12T21:57:48Z |
| format | Article |
| id | doaj.art-ba5bf7aad6c843339056be5bb5e3c690 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-12T21:57:48Z |
| publishDate | 2016-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ba5bf7aad6c843339056be5bb5e3c6902022-12-22T00:10:36ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-09-012016111910.1186/s13660-016-1166-1Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domainCX Guo0YY Chen1YF Guo2Department of Mathematics, China University of Mining and TechnologyDepartment of Mathematics, China University of Mining and TechnologySchool of Science, Guangxi University of Science and TechnologyAbstract In this paper, we first study the deterministic Swift-Hohenberg equation on a bounded domain. After obtaining some a priori estimates by the uniform Gronwall inequality, we prove the existence of an attractor by the Sobolev compact embeddings. Then, we consider the stochastic Swift-Hohenberg equation driven by additive noise on an unbounded domain and prove that the random dynamical system is asymptotically compact by uniform a priori estimates for the far-field values of the solution, which implies the existence of a random attractor for the random dynamical system associated with the stochastic Swift-Hohenberg equation.http://link.springer.com/article/10.1186/s13660-016-1166-1stochastic Swift-Hohenberg equationrandom attractoradditive noiseasymptotically compact |
| spellingShingle | CX Guo YY Chen YF Guo Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain Journal of Inequalities and Applications stochastic Swift-Hohenberg equation random attractor additive noise asymptotically compact |
| title | Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain |
| title_full | Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain |
| title_fullStr | Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain |
| title_full_unstemmed | Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain |
| title_short | Dynamical behaviors of stochastic local Swift-Hohenberg equation on unbounded domain |
| title_sort | dynamical behaviors of stochastic local swift hohenberg equation on unbounded domain |
| topic | stochastic Swift-Hohenberg equation random attractor additive noise asymptotically compact |
| url | http://link.springer.com/article/10.1186/s13660-016-1166-1 |
| work_keys_str_mv | AT cxguo dynamicalbehaviorsofstochasticlocalswifthohenbergequationonunboundeddomain AT yychen dynamicalbehaviorsofstochasticlocalswifthohenbergequationonunboundeddomain AT yfguo dynamicalbehaviorsofstochasticlocalswifthohenbergequationonunboundeddomain |