Effective macroscopic dynamics of stochastic partial differential equations in perforated domains

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dc.creatorWang, Wei
dc.creatorCao, Daomin
dc.creatorDuan, Jinqiao
dc.date2007-03-23
dc.date.accessioned2026-07-07T07:53:26Z
dc.date.available2026-07-07T07:53:26Z
dc.descriptionAn 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.
dc.identifierhttps://arxiv.org/abs/math/0703709
dc.identifierhttp://arxiv.org/abs/math/0703709
dc.identifierSIAM J. Math. Anal., 38 (2007), 1508-1527
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126252
dc.subjectAnalysis of PDEs
dc.subjectDynamical Systems
dc.subjectProbability
dc.subject60H15; 86A05; 34D35
dc.titleEffective macroscopic dynamics of stochastic partial differential equations in perforated domains
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