Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise
Representation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic par...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/2676919 |
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| author | Yanfeng Guo Donglong Li |
| author_facet | Yanfeng Guo Donglong Li |
| author_sort | Yanfeng Guo |
| collection | DOAJ |
| description | Representation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice. |
| format | Article |
| id | doaj-art-95b9d62bcd6642558f7c4b7e2c69d8bc |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-95b9d62bcd6642558f7c4b7e2c69d8bc2025-02-03T01:30:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/26769192676919Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative NoiseYanfeng Guo0Donglong Li1School of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi, 545006, ChinaSchool of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi, 545006, ChinaRepresentation of approximation for manifolds of the stochastic Swift-Hohenberg equation with multiplicative noise has been investigated via non-Markovian reduced system. The approximate parameterizations of the small scales for the large scales are given in the process of seeking for stochastic parameterizing manifolds, which are obtained as pullback limits of some backward-forward systems depending on the time-history of the dynamics of the low modes in a mean square sense through the nonlinear terms. When the corresponding pullback limits of some backward-forward systems are efficiently determined, the corresponding non-Markovian reduced systems can be obtained for researching good modeling performances in practice.http://dx.doi.org/10.1155/2020/2676919 |
| spellingShingle | Yanfeng Guo Donglong Li Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise Advances in Mathematical Physics |
| title | Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise |
| title_full | Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise |
| title_fullStr | Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise |
| title_full_unstemmed | Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise |
| title_short | Representation of Manifolds for the Stochastic Swift-Hohenberg Equation with Multiplicative Noise |
| title_sort | representation of manifolds for the stochastic swift hohenberg equation with multiplicative noise |
| url | http://dx.doi.org/10.1155/2020/2676919 |
| work_keys_str_mv | AT yanfengguo representationofmanifoldsforthestochasticswifthohenbergequationwithmultiplicativenoise AT donglongli representationofmanifoldsforthestochasticswifthohenbergequationwithmultiplicativenoise |