| 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:
|
http://hdl.handle.net/10338.dmlcz/134703 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
