### Abstract

Original language | English |
---|---|

Journal | arXiv |

Publication status | Published - 21 Jul 2018 |

### Fingerprint

### Keywords

- math.DS
- math.AP
- 70K70, 60H15, 60G51

### Cite this

*arXiv*.

**Averaging principles for non-autonomous slow-fast systems of stochastic reaction-diffusion equations with jumps.** / Xu, Yong; Wang, Ruifang; Pei, Bin; Bai, Yuzhen; Kurths, Jürgen.

Research output: Contribution to journal › Article

*arXiv*.

}

TY - JOUR

T1 - Averaging principles for non-autonomous slow-fast systems of stochastic reaction-diffusion equations with jumps

AU - Xu, Yong

AU - Wang, Ruifang

AU - Pei, Bin

AU - Bai, Yuzhen

AU - Kurths, Jürgen

N1 - 30 pages

PY - 2018/7/21

Y1 - 2018/7/21

N2 - 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. So, the Poisson term needs to be processed, and a new method to define the averaged equation needs to be proposed. 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, using the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, using the Khasminskii method, the validity of the averaging principle is verified.

AB - 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. So, the Poisson term needs to be processed, and a new method to define the averaged equation needs to be proposed. 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, using the characteristics of almost periodic functions, the averaged coefficient is defined by the evolution family of measures, and the averaged equation is given. Finally, using the Khasminskii method, the validity of the averaging principle is verified.

KW - math.DS

KW - math.AP

KW - 70K70, 60H15, 60G51

M3 - Article

JO - arXiv

JF - arXiv

ER -