WELL-POSEDNESS, REGULARITY AND EXACT CONTROLLABILITY FOR THE PROBLEM OF TRANSMISSION OF THE SCHRODINGER EQUATION

In this paper, we shall study the system of transmission of the Schrodinger equation with Dirichlet control and colocated observation. Using the multiplier method, we show that the system is well-posed with input and ouput space U = L-2(Gamma) and state space X = H-1(Omega). The regularity of the system is also established, and the feedthrough operator is found to be zero. Finally, the exact controllability of the open-loop system is obtained by proving the observability inequality of the dual system.