On an optimal control problem
The authors apply a finite difference method to the solution of the optimal control problem for an inverse problem for the Schrödinger equation with a final functional of the form \[ J(v)= \int^1_0 (\psi(x, T;v)- y(x))^2dx\to \underset{v\in V}{\text{Infimum}} \] \[ i{\partial\psi\over\partial t}+ a_0{\partial^2\psi\over\partial x^2}- a(x)\psi- v(t)\psi= f(x, t), \] \[ \psi(x,0)= \varphi(x),\quad x\in(0, 1);\quad {\partial\psi(0, t)\over\partial x}= {\partial\psi(1, t)\over \partial x}= 0,\quad t\in (0,T). \] The convergence of the difference approximation is proved and an application is given.
scientific article; zbMATH DE number 1145894
scientific article