ASYMPTOTIC EXPANSION AND CONVERGENCE THEOREM OF CONTROL AND OBSERVATION ON THE BOUNDARY FOR SECOND-ORDER ELLIPTIC EQUATION WITH HIGHLY OSCILLATORY COEFFICIENTS

In this paper, we shall study systems governed by the Neumann problem of second-order elliptic equation with rapidly oscillating coefficients and with control and observations on the boundary. The multiscale asymptotic expansions of the solution for considering problem in the case without any constraints, and homogenized equation in the case with constraints will be given, their rigorous proofs will also be proposed.