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A thick junction is a singurlarly pertubed domain in Rn with periodic structure, which depends on a small parameter. Thick junctions are prototypes of many physical (various types of radiators, frameworks of buildings, spaceship grids, etc.) and biological systems (viruses, etc.).

Strict definition and examples of thick junctions
A thick junction of type l:m:n is the union of some domain (called a junction's body) and many thin domains that are ε-periodically attached to some manifold on the boundary of the junction's body. This manifold is called the joint zone. Here ε is a small parameter characterizing the number of the attached thin domains, distance between the neighboring thin domains and also their thickness. The type l:m:n of the thick junction indicates the limiting dimensions (as ε tends to zero) of the junction's body (l), the joint zone (m), and each of the attached thin domains (n) respectively (this classification was given in papers by T.A. Mel'nyk and S.A. Nazarov).

Examples  types

Boundary value problems in thick junctions
Various constructions of thick junction type are successfully used in nanotechnologies and microtechnics (cf., for example, \cite{Len}, \cite{Lysh}), which caused the extensive study of boundary value problems in thick junctions and in other more complicated domains (cf., for example, \cite{Am-Ch-Gad}-\cite{B-G-M}, \cite{Ch-M}, \cite{M-Nak-W} and references therein).

Since the increase of the attached thin domains of a thick junction naturally leads to longer computing time, it is often impossible to obtain computational solutions to boundary value problems in such domains with sufficient accuracy. Therefore asymptotical analysis is used in such cases. The main aim of the asymptotical analysis of boundary value problems in thick junctions is to develop rigorous asymptotic methods for boundarynvalue problems in thick junctions of different types as ε → 0, i.e. when the number of the attached thin domains infinitely increases and their thickness tends to zero.

Boundary value problems in thick singularly degenerating junctions have specific difficulties and require special approaches.