Asymptotic approximation of solution to quasilinear elliptic boundary-value problem in a two-level thick junction of type 3:2:2

Abstract

We consider quasilinear elliptic boundary-value problem in atwo-level thick junction $Omega_varepsilon$ of type $3:2:2$, which is theunion of a cylinder $Omega_0$ and a large number of $varepsilon$-periodicallysituated thin discs with varying thickness. Different Robin boundary conditionswith perturbed parameters are given on the surfaces of the thin discs. Theleading terms of the asymptotic expansion are constructed and the correspondingestimate in Sobolev space is obtained.