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Journal of Nonlinear Science

, Volume 29, Issue 4, pp 1701–1759 | Cite as

Averaging Principle for Multiscale Stochastic Klein–Gordon-Heat System

  • Peng GaoEmail author
Article
  • 119 Downloads

Abstract

This paper investigates multiscale stochastic Klein–Gordon-heat system. We establish the well-posedness and two kinds of stochastic averaging principle for stochastic Klein–Gordon-heat system with two timescales. To be more precise, under suitable conditions, two kinds of averaging principle (the autonomous case and the nonautonomous case) are proved, and as a consequence, the multiscale stochastic Klein–Gordon-heat system can be reduced to a single stochastic Klein–Gordon equation (averaged equation) with a modified coefficient, the slow component of multiscale stochastic system toward the solution of the averaged equation in moment (the autonomous case) and in probability (the nonautonomous case).

Keywords

Multiscale stochastic partial differential equations Stochastic averaging principle Stochastic Klein–Gordon-heat system Stochastic Klein–Gordon equation Effective dynamics 

Mathematics Subject Classification

60H15 70K65 70K70 37H10 37L55 

Notes

Acknowledgements

I would like to thank the referees and the editor for their careful comments and useful suggestions. I sincerely thank Professor Yong Li for many useful suggestions and help.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchunPeople’s Republic of China

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