Homogenization of 3D Thick Cascade Junction with a Random Transmission Zone Periodic in One direction

In the paper, we deal with the homogenization problem for the Poisson equation in a singularly perturbed three-dimensional junction of a new type. This junction consists of a body and a large number of thin curvilinear cylinders, joining to body through a random transmission zone with rapidly oscillating boundary, periodic in one direction. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and with random perturbed coefficients on the boundary of the transmission zone. We prove the homogenization theorems and the convergence of the energy integrals.