Geodesic
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
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 23-28

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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 $\varepsilon$-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 $\partial\Omega$.
Keywords: homogenization, rapidly oscillating boundary conditions, dynamic boundary conditions. 
@article{DANMA_2020_491_a4,
     author = {J. I. Diaz and D. G\'omez-Castro and T. A. Shaposhnikova and M. N. Zubova},
     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},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {23--28},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a4/}
}
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J. I. Diaz; D. Gómez-Castro; T. A. Shaposhnikova; M. N. Zubova. 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. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 23-28. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a4/