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https://hdl.handle.net/2440/55775
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Type: | Journal article |
Title: | Effective macroscopic dynamics of stochastic partial differential equations in perforated domains |
Author: | Wang, W. Cao, D. Duan, J. |
Citation: | SIAM Journal on Mathematical Analysis, 2006; 38(5):1508-1527 |
Publisher: | Siam Publications |
Issue Date: | 2006 |
ISSN: | 0036-1410 1095-7154 |
Statement of Responsibility: | Wei Wang, Daomin Cao and Jinqiao Duan |
Abstract: | An effective macroscopic model for a stochastic microscopic system is derived. The original microscopic system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes or heterogeneities. The homogenized effective model is still a stochastic partial differential equation but defined on a unified domain without holes. The solutions of the microscopic model is shown to converge to those of the effective macroscopic model in probability distribution, as the size of holes diminishes to zero. Moreover, the long time effectivity of the macroscopic system in the sense of \emph{convergence in probability distribution}, and the effectivity of the macroscopic system in the sense of \emph{convergence in energy} are also proved. |
Keywords: | Mathematics - Analysis of PDEs Mathematics - Dynamical Systems Mathematics - Probability 60H15 86A05 34D35 |
Rights: | Copyright © 2006. Siam Publications All rights reserved. |
DOI: | 10.1137/050648766 |
Published version: | http://dx.doi.org/10.1137/050648766 |
Appears in Collections: | Aurora harvest Mathematical Sciences publications |
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