Higher order asymptotics of solutions of problems on the contact of periodic structures

A methodology is proposed for averaging in boundary value problems with plane bondary, and also problems on the contact of several microstructures with plane contact surface. Boundary layers are taken into account in this methodology. The author considers both direct contact of two structures and contact of two media separated by a thin inhomogeneous layer having periodic structure. Formal asymptotic solutions of some problems on the contact of two media are constructed, and estimates of how close the asymptotic solution is to the exact solution are derived.
Bibliography: 34 titles.