Homogenization of a Singularly Perturbed Parabolic Problem in a Thick Periodic Junction of the Type 3:2:1

Abstract

We prove a convergence theorem and obtain asymptotic (as ε → 0) estimates for a solution of a parabolic initial boundary-value problem in a junction Ω_ε that consists of a domain Ω₀ and a large number N ² of ε-periodically located thin cylinders whose thickness is of order ε = O(N ⁻¹).