Mel’nyk, T. A.; Chechkin, G. A. Asymptotic analysis of boundary-value problems in thick cascade junctions. (Russian. English summary) Zbl 1164.35316 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 9, 16-22 (2008). Summary: We consider the homogenization problem in a singularly perturbed two-dimensional domain of a new type, which consists of a body of junction and a great number of alternating thin rods belonging to two classes. Under the assumptions that one class consists of rods of finite length and the other consists of rods of small length, and that inhomogeneous Fourier boundary conditions (boundary conditions of the third type) with perturbed coefficients are set on the boundaries of thin rods, we prove the homogenization theorems and the convergence of the energy integrals. Cited in 4 Documents MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35B40 Asymptotic behavior of solutions to PDEs 35C20 Asymptotic expansions of solutions to PDEs Keywords:cascade junction; boundary-value problem; homogenization problem PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{G. A. Chechkin}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 9, 16--22 (2008; Zbl 1164.35316)