Asymptotic Analysis of the Neumann Problem for the Ukawa Equation in a Thick Multi-structure of Type 3:2:2

Abstract

We propose two different approaches for asymptotic analysis of the Neumann boundary-value problem for the Ukawa equation in a thick multistructure Ω _ε , which is the union of a domain Ω₀ and a large number N of ε—periodically situated thin annular disks with variable thickness of order $\varepsilon = \mathcal{O}\left( {N^{ - 1} } \right)$, as ε → 0. In the first approach, using some special extension operator, the convergence theorem is proved as ε → 0. In the second one, the leading terms of the asymptotic expansion for the solution are constructed and the corresponding estimates in the Sobolev space H¹(Ωε) are proved.