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

We consider a quasilinear parabolic boundary-value problem in a two-level thick junction $Omega_varepsilon$ of type $3:2:2$, which is the union of a cylinder $Omega_0$ and a large number of $varepsilon$-periodically situated thin discs with variable thickness. Different Robin boundary conditions with perturbed parameters are given on the surfaces of the thin discs. The leading terms of the asymptotic expansion are constructed and the corresponding estimate in Sobolev space is obtained.