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.