Homogenization and localization with an interface
We consider the homogenization of a spectral problem for a diffusion equation posed in a singularly perturbed periodic medium. Denoting by ε the period, the diffusion coefficients are scaled as ε2. The domain is composed of two periodic medium separated by a planar interface, aligned with the period...
| Հիմնական հեղինակներ: | , , |
|---|---|
| Ձևաչափ: | Journal article |
| Լեզու: | English |
| Հրապարակվել է: |
2003
|
| _version_ | 1826306066757976064 |
|---|---|
| author | Allaire, G Capdeboscq, Y Piatnitski, A |
| author_facet | Allaire, G Capdeboscq, Y Piatnitski, A |
| author_sort | Allaire, G |
| collection | OXFORD |
| description | We consider the homogenization of a spectral problem for a diffusion equation posed in a singularly perturbed periodic medium. Denoting by ε the period, the diffusion coefficients are scaled as ε2. The domain is composed of two periodic medium separated by a planar interface, aligned with the periods. Three different situations arise when ε goes to zero. First, there is a global homogenized problem as if there were no 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 | 2024-03-07T06:42:18Z |
| format | Journal article |
| id | oxford-uuid:f9b8002e-fb73-4fe9-aa1d-7dabe0a4c966 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:42:18Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:f9b8002e-fb73-4fe9-aa1d-7dabe0a4c9662022-03-27T12:59:54ZHomogenization and localization with an interfaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f9b8002e-fb73-4fe9-aa1d-7dabe0a4c966EnglishSymplectic Elements at Oxford2003Allaire, GCapdeboscq, YPiatnitski, AWe consider the homogenization of a spectral problem for a diffusion equation posed in a singularly perturbed periodic medium. Denoting by ε the period, the diffusion coefficients are scaled as ε2. The domain is composed of two periodic medium separated by a planar interface, aligned with the periods. Three different situations arise when ε goes to zero. First, there is a global homogenized problem as if there were no 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 Piatnitski, A Homogenization and localization with an interface |
| title | Homogenization and localization with an interface |
| title_full | Homogenization and localization with an interface |
| title_fullStr | Homogenization and localization with an interface |
| title_full_unstemmed | Homogenization and localization with an interface |
| title_short | Homogenization and localization with an interface |
| title_sort | homogenization and localization with an interface |
| work_keys_str_mv | AT allaireg homogenizationandlocalizationwithaninterface AT capdeboscqy homogenizationandlocalizationwithaninterface AT piatnitskia homogenizationandlocalizationwithaninterface |