| Title:
|
Stochastic homogenization of a class of monotone eigenvalue problems (English) |
| Author:
|
Svanstedt, Nils |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
55 |
| Issue:
|
5 |
| Year:
|
2010 |
| Pages:
|
385-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Stochastic homogenization (with multiple fine scales) is studied for a class of nonlinear monotone eigenvalue problems. More specifically, we are interested in the asymptotic behaviour of a sequence of realizations of the form $$ -\div \Bigl (a\Bigl (T_1\Bigl (\frac x{\varepsilon _1}\Bigr )\omega _1,T_2 \Bigl (\frac x{\varepsilon _2}\Bigr )\omega _2, \nabla u^\omega _{\varepsilon }\Bigr )\Bigr ) =\lambda _\varepsilon ^\omega \mathcal C(u^\omega _{\varepsilon }). $$ It is shown, under certain structure assumptions on the random map $a(\omega _1,\omega _2,\xi )$, that the sequence $\{\lambda _\varepsilon ^{\omega ,k},u^{\omega ,k}_\varepsilon \}$ of $k$th eigenpairs converges to the $k$th eigenpair $\{\lambda ^k,u^k\}$ of the homogenized eigenvalue problem $$ - {\rm div}( b(\nabla u) ) = \lambda {\overline {\mathcal C}}(u). $$ For the case of $p$-Laplacian type maps we characterize $b$ explicitly. (English) |
| Keyword:
|
stochastic |
| Keyword:
|
homogenization |
| Keyword:
|
eigenvalue |
| MSC:
|
35B27 |
| MSC:
|
35B40 |
| MSC:
|
35J25 |
| MSC:
|
35J62 |
| MSC:
|
35J92 |
| MSC:
|
35P30 |
| idZBL:
|
Zbl 1224.35026 |
| idMR:
|
MR2737719 |
| DOI:
|
10.1007/s10492-010-0014-8 |
| . |
| Date available:
|
2010-11-24T08:14:18Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140711 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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