Approximation of a control problem for a nonlinear equation of Schrödinger type (Q1109328)

This paper is concerned with the minimization of the integral functional defined on solutions of the first boundary-value problem for a Schrödinger equation with cubic nonlinearity. The control is defined as the initial state subject to integral constraints. For finite-dimensional approximations of the problem constructed with the projection-difference method, an estimate of the speed of convergence with respect to the functional is obtained. Approximating problems are regularized by using the Tikhonov method to obtain convergence in the control actions.