Imperfect transmission problems: homogenization with weakly converging data

Abstract The aim of the talk is to describe the asymptotic behavior, as " ! 0, of an elliptic problem with rapidly oscillating coecients in an "-periodic two component composite with imperfect inclusions of size ". On the interface we prescribe a jump of the solution proportional to the conormal derivative by means of a function of order ". This work extends to the case of weakly converging data some previous results by P. Donato and S. Monsurro, obtained when a xed datum or strongly converging data are considered. This homogenization result, interesting in itself, could have useful applica- tions in the study of the exact controllability of a hyperbolic problem set in the same kind of domain and with the same jump condition on the interface. Indeed, when studying the exact controllability, via HUM method, one needs to exploit some homogenization results applied to a transposed problem. To do that, it is necessary to study the asymptotic behavior of a stationary problem, with weakly converging data. References [1] L. Faella, S. Monsurro, C. Perugia, Homogenization of imperfect trans- mission problems: the case of weakly converging data, Dierential Integral Equations, to appear