Averaging in cascade junctions with a “wide” transmission domain

We consider a boundary-value problem for the Poisson equation in a dense multilevel junction consisting of a body of the junction and many periodically situated thin rectangles connected with the body by a transmission layer with a periodic boundary. It is supposed that the rectangles have finite lengths and the transmission layer has a small width that is much greater than the period. Nonhomogeneous Neumann boundary conditions are imposed upon the boundary of the transmission layer. An addition parameter of perturbation is included in these boundary conditions. Averaged problems are constructed and convergence theorems for solution and energy integrals are proved as a function of that parameter.