Homogenization of the Neumann–Fourier Problem in a Thick Two-Level Junction of Type 3:2:1

Анотація

We consider a mixed boundary-value problem for the Poisson equation in a two-level junction $\Omega_\varepsilon$ which is the union of a domain $\Omega_0$ and a large number of thin cylinders with cross-section of order $\mathcal{O}(\varepsilon^2)$. The thin cylinders are divided into two levels depending on their lengths. In addition, the thin cylinders from each level are $\varepsilon$-periodically alternated. The nonuniform Neumann conditions are given on the lateral sides of the thin cylinders from the first level and the uniform Fourier conditions are given on the lateral sides of the thin cylinders from the second level. We study the asymptotic behavior of the solution as $\varepsilon\to 0$. The convergence theorem and the convergence of the energy integral are proved.

Mathematics Subject Classification: 35B27, 35J25, 35C20, 35B25.