Multi-structures: asymptotic analysis and singular perturbation problems

This review paper gives an outline of mathematical models of multi-structures. The approach is based on an asymptotic analysis of a class of elliptic boundary value problems posed in singularly perturbed domains. A particular attention is given to formulation of the “junction conditions” to link different parts of the multi-structure. The paper also discusses a range of applications of this asymptotic theory in physics and mechanics.