On an optimal control problem
type: Item
instance of: scholarly article
title: On an optimal control problem
zbMATH Open document ID: 0898.65033
DOI: 10.1016/S0377-0427(97)00198-2
published in: Journal of Computational and Applied Mathematics
publication date: 1998-04-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 1145894
zbMATH Keywords: finite difference method
zbMATH Keywords: optimal control problem
zbMATH Keywords: inverse problem
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: convergence
author: Bunyamin Yildiz
author: Gabil Yagubov
reviewed by: Hans Benker
MaRDI profile type: Publication
cites work: Bounds for a class of linear functionals with applications to Hermite interpolation
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cites work: Problemi di Cauchy e problemi ai limiti per equazioni di evoluzione del tipo di Schrödinger lineari e non lineari. Parte II
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description: scientific article; zbMATH DE number 1145894