**Abstract: **We will discuss the asymptotic tools for the construction of asymptotic
expansions of the solutions of the partial differential equations set in
thin domains, such as , for example, a connected union of two thin
rectangles (a cross-shaped domain). The thickness of the rectangles is a
small parameter (if their length is of order of 1). The techniques is
similar to the homogenization and to the boundary layer method. The talk
is based on the results presented in

1. the book: Panasenko G. "Multi-Scale Modelling for Structures and
Composites", Springer, 2005, 398 pp.

2. the paper: Panasenko G., Perez E."Asymptotic partial decomposition of
domain for spectral problems in rod structures"
J.Math.Pures Appl., 87,2007, pp.1-36.