| Title:
|
Homogenization of linear parabolic equations with three spatial and three temporal scales for certain matchings between the microscopic scales (English) |
| Author:
|
Danielsson, Tatiana |
| Author:
|
Johnsen, Pernilla |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
4 |
| Year:
|
2021 |
| Pages:
|
483-511 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^{2}(0,T;H_{0}^{1}(\Omega ))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic partial differential equation $\varepsilon ^{p}\partial _{t}u_{\varepsilon }(x,t) -\nabla \cdot ( a( x\varepsilon ^{-1} ,x\varepsilon ^{-2},t\varepsilon ^{-q},t\varepsilon ^{-r}) \nabla u_{\varepsilon }(x,t) ) = f(x,t) $, where $0<p<q<r$. The homogenization result reveals two special phenomena, namely that the homogenized problem is elliptic and that the matching for which the local problem is parabolic is shifted by $p$, compared to the standard matching that gives rise to local parabolic problems. (English) |
| Keyword:
|
homogenization |
| Keyword:
|
parabolic problem |
| Keyword:
|
multiscale convergence |
| Keyword:
|
very weak multiscale convergence |
| Keyword:
|
two-scale convergence |
| MSC:
|
35B27 |
| MSC:
|
35K20 |
| idZBL:
|
Zbl 07442515 |
| idMR:
|
MR4336552 |
| DOI:
|
10.21136/MB.2021.0087-19 |
| . |
| Date available:
|
2021-11-08T16:22:12Z |
| Last updated:
|
2021-12-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149262 |
| . |
| Reference:
|
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