A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case
A strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is considered. A problem with dynamic boundary conditions given on the union of some boundary subsets of critical size arranged ε-periodic...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2020
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| _version_ | 1826298578406998016 |
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| author | Díaz, JI Gómez-Castro, D Shaposhnikova, TA Zubova, MN |
| author_facet | Díaz, JI Gómez-Castro, D Shaposhnikova, TA Zubova, MN |
| author_sort | Díaz, JI |
| collection | OXFORD |
| description | A strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is considered. A problem with dynamic boundary conditions given on the union of some boundary subsets of critical size arranged ε-periodically along the boundary and with homogeneous Neumann conditions given on the rest of the boundary is studied. It is proved that the homogenized boundary condition is a Robin-type containing a nonlocal term depending on the trace of the solution u(x, t) on the boundary ∂Ω. |
| first_indexed | 2024-03-07T04:49:00Z |
| format | Journal article |
| id | oxford-uuid:d44e4224-ba7b-4764-a046-40d2ae9330cf |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:49:00Z |
| publishDate | 2020 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:d44e4224-ba7b-4764-a046-40d2ae9330cf2022-03-27T08:17:36ZA time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical caseJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d44e4224-ba7b-4764-a046-40d2ae9330cfEnglishSymplectic ElementsSpringer2020Díaz, JIGómez-Castro, DShaposhnikova, TAZubova, MNA strange term arising in the homogenization of elliptic (and parabolic) equations with dynamic boundary conditions given on some boundary parts of critical size is considered. A problem with dynamic boundary conditions given on the union of some boundary subsets of critical size arranged ε-periodically along the boundary and with homogeneous Neumann conditions given on the rest of the boundary is studied. It is proved that the homogenized boundary condition is a Robin-type containing a nonlocal term depending on the trace of the solution u(x, t) on the boundary ∂Ω. |
| spellingShingle | Díaz, JI Gómez-Castro, D Shaposhnikova, TA Zubova, MN A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title | A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title_full | A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title_fullStr | A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title_full_unstemmed | A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title_short | A time-dependent strange term arising in homogenization of an elliptic problem with rapidly alternating Neumann and dynamic boundary conditions specified at the domain boundary: The critical case |
| title_sort | time dependent strange term arising in homogenization of an elliptic problem with rapidly alternating neumann and dynamic boundary conditions specified at the domain boundary the critical case |
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