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

Yong Xu, Ruifang Wang, Bin Pei, Yuzhen Bai, Jürgen Kurths

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
JournalarXiv
Publication statusPublished - 21 Jul 2018

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Stochastic Reaction-diffusion Equations
Slow-fast System
Averaging Principle
Nonautonomous Systems
Jump
Evolution Family
Almost Periodic
Poisson Random Measure
Almost Periodic Functions
Coefficient
Siméon Denis Poisson
Term

Keywords

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

Cite this

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.

In: arXiv, 21.07.2018.

Research output: Contribution to journalArticle

Xu, Yong ; Wang, Ruifang ; Pei, Bin ; Bai, Yuzhen ; Kurths, Jürgen. / Averaging principles for non-autonomous slow-fast systems of stochastic reaction-diffusion equations with jumps. In: arXiv. 2018.
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