Homogenization of a boundary condition for the heat equation (Q1585702)

In a cylindric domain there is considered the equation \(\partial_t u_{\varepsilon} -\Delta u_{\varepsilon} =f_{\varepsilon}(x,t)\) together with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann types. The authors study asymptotic behavior of \(u_{\varepsilon}\), including the effect of the Neumann conditions in the second-order term of the asymptotic expansion.