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Type: | Journal article |
Title: | Macroscopic reduction for stochastic reaction-diffusion equations |
Author: | Wang, W. Roberts, A. |
Citation: | IMA Journal of Applied Mathematics, 2013; 78(6):1237-1264 |
Publisher: | Oxford Univ Press |
Issue Date: | 2013 |
ISSN: | 0272-4960 1464-3634 |
Department: | Faculty of Engineering, Computer & Mathematical Sciences |
Statement of Responsibility: | W. Wang and A. J. Roberts |
Abstract: | The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic reaction-diffusion equations with cubic nonlinearity by artificial separating the system into two distinct slow-fast time parts. An averaging method and a deviation estimate show that the macroscopic reduced model should be a stochastic ordinary equation which includes the random effect transmitted from the microscopic timescale due to the nonlinear interaction. Numerical simulations of an example stochastic heat equation confirms the predictions of this stochastic modelling theory. This theory empowers us to better model the long time dynamics of complex stochastic systems. |
Keywords: | stochastic reaction–diffusion equations averaging tightness martingale |
Rights: | © The authors 2012. |
DOI: | 10.1093/imamat/hxs019 |
Grant ID: | http://purl.org/au-research/grants/arc/DP0774311 http://purl.org/au-research/grants/arc/DP0988738 http://purl.org/au-research/grants/arc/DP0988738 http://purl.org/au-research/grants/arc/DP0774311 |
Published version: | http://dx.doi.org/10.1093/imamat/hxs019 |
Appears in Collections: | Aurora harvest 4 Mathematical Sciences publications |
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