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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 1029-242X |