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 |
| Published: |
Springer
2020
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| Summary: | 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. |
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