Asymptotic Solution to a Mixed Boundary-Value Problem in a Thick Multi-Structure of Type 3:2:2

Abstract

The leading terms of the asymptotic expansion for the solution to a mixed boundary value problem for the Poisson equation in a thick multi-structure, which is the union of some domain and a large number N of ε-periodically situated thin annular disks with variable thickness of order ε = O(N⁻¹), are constructed and the corresponding estimates in the Sobolev space H¹ are proved as ε → 0.