Asymptotic analysis of a boundary-value problem in a cascade thick junction with a random transmission zone
Gregory Aleksandrovich Chechkin, T. P. Chechkina, Ciro D’Apice, Umberto De Maio, Taras Mel’nyk · Applicable Analysis · 2009
In the article we deal with the homogenization of a boundary-value problem for the Poisson equation in a singularly perturbed two-dimensional junction of a new type. This junction consists of a body and a large number of thin rods, which join the body through the random transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin rods and with random perturbed coefficients on the boundary of the transmission zone. We prove the homogenization theorems and the convergence of the energy integrals. It is shown that there are three qualitatively different cases in the asymptotic behaviour of the solutions.