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 - Díaz, JI; Gómez-Castro, D; Shaposhnikova, TA; Zubova, MN (Springer, 2020)
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.