| Abstract: | This paper is devoted to the study of the asymptotic behavior of the solutions of singularly perturbed transmission problems in a periodically perforated domain. The domain is obtained by making in  a periodic set of holes, each of them of size proportional to a positive parameter ε. We first consider an ideal transmission problem and investigate the behavior of the solution as ε tends to 0. In particular, we deduce a representation formula in terms of real analytic maps of ε and of some additional parameters. Then we apply such result to a nonideal nonlinear transmission problem. |
