Asymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions
Taras Mel’nyk, Gregory Aleksandrovich Chechkin · Sbornik Mathematics · 2009
We consider homogenization problems in a singularly perturbed three-dimensional domain of multi-level-junction type which consists of the junction body and a large number of alternating thin curvilinear cylinders that belong to two classes. Under the assumption that one class consists of cylinders of finite height, and the second class of cylinders of infinitesimal height, and that different inhomogeneous boundary conditions of the third kind with perturbed coefficients are given on the boundaries of the thin curvilinear cylinders, we prove the homogenization theorems and the convergence of the energy integrals. Bibliography: 42 titles.