Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump
In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of them are periodic or almost periodic. Therefore, the Poisson...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/9864352 |
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| author | Yong Xu Ruifang Wang |
| author_facet | Yong Xu Ruifang Wang |
| author_sort | Yong Xu |
| collection | DOAJ |
| description | In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of them are periodic or almost periodic. Therefore, the Poisson term needs to be processed, and a new averaged equation needs to be given. For this reason, the existence of time-dependent evolution family of measures associated with the fast equation is studied and proved that it is almost periodic. Next, according to the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, the validity of the averaging principle is verified by using the Khasminskii method. |
| format | Article |
| id | doaj-art-8bfc73aec88c4eef822356f25782e9fb |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8bfc73aec88c4eef822356f25782e9fb2025-02-03T01:01:52ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/98643529864352Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with JumpYong Xu0Ruifang Wang1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaDepartment of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, ChinaIn this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. The coefficients of the equation are assumed to be functions of time, and some of them are periodic or almost periodic. Therefore, the Poisson term needs to be processed, and a new averaged equation needs to be given. For this reason, the existence of time-dependent evolution family of measures associated with the fast equation is studied and proved that it is almost periodic. Next, according to the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, the validity of the averaging principle is verified by using the Khasminskii method.http://dx.doi.org/10.1155/2020/9864352 |
| spellingShingle | Yong Xu Ruifang Wang Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump Complexity |
| title | Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump |
| title_full | Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump |
| title_fullStr | Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump |
| title_full_unstemmed | Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump |
| title_short | Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump |
| title_sort | averaging principles for nonautonomous two time scale stochastic reaction diffusion equations with jump |
| url | http://dx.doi.org/10.1155/2020/9864352 |
| work_keys_str_mv | AT yongxu averagingprinciplesfornonautonomoustwotimescalestochasticreactiondiffusionequationswithjump AT ruifangwang averagingprinciplesfornonautonomoustwotimescalestochasticreactiondiffusionequationswithjump |