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Title: Multiscale stochastic homogenization of convection-diffusion equations (English)
Author: Svanstedt, Nils
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 53
Issue: 2
Year: 2008
Pages: 143-155
Summary lang: English
Category: math
Summary: Multiscale stochastic homogenization is studied for convection-diffusion problems. More specifically, we consider the asymptotic behaviour of a sequence of realizations of the form ${\partial u^\omega _{\varepsilon }}/{\partial t} +{1}/{\epsilon _3}\,\mathcal C\bigl (T_3({x}/{\varepsilon _3}) \omega _3\bigr )\cdot \nabla u^\omega _{\varepsilon }- \div \bigl ( \alpha \bigl (T_1({x}/{\varepsilon _1})\omega _1, T_2({x}/{\varepsilon _2})\omega _2 ,t\bigr ) \nabla u^\omega _{\varepsilon }\bigr )=f$. It is shown, under certain structure assumptions on the random vector field ${\mathcal C}(\omega _3)$ and the random map $\alpha (\omega _1,\omega _2,t)$, that the sequence $\lbrace u^\omega _\epsilon \rbrace $ of solutions converges in the sense of G-convergence of parabolic operators to the solution $u$ of the homogenized problem ${\partial u}/{\partial t} - \div ( \mathcal B(t)\nabla u ) = f$. (English)
Keyword: multiscale
Keyword: stochastic
Keyword: homogenization
Keyword: convection-diffusion
MSC: 35B27
MSC: 35B40
MSC: 35K57
MSC: 60H15
MSC: 76M35
MSC: 76M50
idZBL: Zbl 1199.35017
idMR: MR2399903
DOI: 10.1007/s10492-008-0017-x
Date available: 2009-09-22T18:32:41Z
Last updated: 2020-07-02
Stable URL:
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