APPROXIMATE CONTROLLABILITY OF A SEMILINEAR ELLIPTIC PROBLEM WITH ROBIN CONDITION IN A PERIODICALLY PERFORATED DOMAIN.

In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem. [ABSTRACT FROM AUTHOR]