Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface
In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by (Epsilon) the period, the diffusion coefficient is scaled as (Epsilon). The domain is made of two purely periodic media separated by an interfa...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer-Verlag
2002
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| _version_ | 1797077990106988544 |
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| author | Allaire, G Capdeboscq, Y |
| author_facet | Allaire, G Capdeboscq, Y |
| author_sort | Allaire, G |
| collection | OXFORD |
| description | In one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by (Epsilon) the period, the diffusion coefficient is scaled as (Epsilon). The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when (Epsilon) goes to zero. First, there is a global homogenized problem as in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunction. |
| first_indexed | 2024-03-07T00:25:59Z |
| format | Journal article |
| id | oxford-uuid:7e265c14-c8de-4f74-9cf5-9ed811d20009 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:25:59Z |
| publishDate | 2002 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:7e265c14-c8de-4f74-9cf5-9ed811d200092022-03-26T21:08:25ZHomogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interfaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7e265c14-c8de-4f74-9cf5-9ed811d20009EnglishSymplectic Elements at OxfordSpringer-Verlag2002Allaire, GCapdeboscq, YIn one space dimension we address the homogenization of the spectral problem for a singularly perturbed diffusion equation in a periodic medium. Denoting by (Epsilon) the period, the diffusion coefficient is scaled as (Epsilon). The domain is made of two purely periodic media separated by an interface. Depending on the connection between the two cell spectral equations, three different situations arise when (Epsilon) goes to zero. First, there is a global homogenized problem as in the case without an interface. Second, the limit is made of two homogenized problems with a Dirichlet boundary condition on the interface. Third, there is an exponential localization near the interface of the first eigenfunction. |
| spellingShingle | Allaire, G Capdeboscq, Y Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title | Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title_full | Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title_fullStr | Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title_full_unstemmed | Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title_short | Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface |
| title_sort | homogenization and localization for a 1 d eigenvalue problem in a periodic medium with an interface |
| work_keys_str_mv | AT allaireg homogenizationandlocalizationfora1deigenvalueprobleminaperiodicmediumwithaninterface AT capdeboscqy homogenizationandlocalizationfora1deigenvalueprobleminaperiodicmediumwithaninterface |