Optimal bilinear control of the coupled nonlinear Schrödinger system. (June 2019) - Wang, Kai; Zhao, Dun; Feng, Binhua
Abstract: We investigate the optimal bilinear control problem governed by the coupled nonlinear Schrödinger systems with Coulombian potential in R 3 . The existence of the optimal control with initial data in H 1 is presented by weak convergence method, and the Fréchet-differentiability of the objective functional with respect to the control is obtained based on H 2 regularity. Furthermore, the first-order optimality system is rigorously derived. Our results have improved some recent works.