Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities

A boundary-value problem for a second-order elliptic equation with variable coefficients is considered in a multidimensional domain with periodic perforation by small cavities arranged along a fixed hypersurface at small distances one from another. The distances are proportional to a small parameter epsilon, and the linear sizes of the cavities are proportional to epsilon eta(epsilon), where eta(epsilon) is a function taking values in the interval [0, 1]. The main result is a complete asymptotic expansion for the solution of the perturbed problem. The asymptotic expansion is a combination of an outer and an inner expansion; it is constructed using the method of matched asymptotic expansions. Both outer and inner expansions are power expansions in epsilon with coefficients depending on eta. These coefficients are shown to be infinitely differentiable with respect to eta is an element of (0, 1] and uniformly bounded in eta is an element of [0, 1]. Bibliography: 38 titles.