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Open Access Research

Optimal control problem for stationary quasi-optic equations

Yusuf Koçak1* and Ercan Çelik2

Author Affiliations

1 Department of Mathematics, Ağrı İbrahim Çeçen University Faculty of Science and Art, Ağrı, Turkey

2 Department of Mathematics, Atatürk University Faculty of Science, Erzurum, Turkey

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Boundary Value Problems 2012, 2012:151  doi:10.1186/1687-2770-2012-151

Published: 28 December 2012

Abstract

In this paper, an optimal control problem was taken up for a stationary equation of quasi optic. For the stationary equation of quasi optic, at first judgment relating to the existence and uniqueness of a boundary value problem was given. By using this judgment, the existence and uniqueness of the optimal control problem solutions were proved. Then we state a necessary condition to an optimal solution. We proved differentiability of a functional and obtained a formula for its gradient. By using this formula, the necessary condition for solvability of the problem is stated as the variational principle.

Keywords:
stationary equation of quasi optic; boundary value problem; optimal control problem; variational problem