Homogenization of a quasilinear parabolic problem with different alternating nonlinear Fourier boundary conditions in a two-level thick junction of the type 3:2:2

Abstract

We investigate the asymptotic behavior of a solution of a quasilinear parabolic boundary-value problem in a two-level thick junction of the type 3:2:2. This junction consists of a cylinder on which thin disks of variable thickness are $\varepsilon$-periodically threaded. The thin disks are divided into two levels, depending on their geometric structure and the conditions imposed on their boundaries. In this problem, we consider different alternating inhomogeneous nonlinear Fourier conditions. Moreover, the Fourier conditions depend on additional perturbation parameters. We prove theorems on the convergence of a solution of this problem as $\varepsilon \rightarrow 0$ for different values of these parameters.