A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales
We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/329704 |
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| _version_ | 1832561210392838144 |
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| author | Liselott Flodén Anders Holmbom Marianne Olsson Lindberg Jens Persson |
| author_facet | Liselott Flodén Anders Holmbom Marianne Olsson Lindberg Jens Persson |
| author_sort | Liselott Flodén |
| collection | DOAJ |
| description | We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear. |
| format | Article |
| id | doaj-art-35768dc3ddd9433a9ddbb7aafc5399a0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-35768dc3ddd9433a9ddbb7aafc5399a02025-02-03T01:25:40ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/329704329704A Note on Parabolic Homogenization with a Mismatch between the Spatial ScalesLiselott Flodén0Anders Holmbom1Marianne Olsson Lindberg2Jens Persson3Department of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, 83125 Östersund, SwedenDepartment of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, 83125 Östersund, SwedenDepartment of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, 83125 Östersund, SwedenDepartment of Quality Technology and Management, Mechanical Engineering and Mathematics, Mid Sweden University, 83125 Östersund, SwedenWe consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.http://dx.doi.org/10.1155/2013/329704 |
| spellingShingle | Liselott Flodén Anders Holmbom Marianne Olsson Lindberg Jens Persson A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales Abstract and Applied Analysis |
| title | A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales |
| title_full | A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales |
| title_fullStr | A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales |
| title_full_unstemmed | A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales |
| title_short | A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales |
| title_sort | note on parabolic homogenization with a mismatch between the spatial scales |
| url | http://dx.doi.org/10.1155/2013/329704 |
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