Journal of Applied Mathematics
Volume 2012 (2012), Article ID 672947, 25 pages
http://dx.doi.org/10.1155/2012/672947
Research Article

Optimality Conditions for Infinite Order Distributed Parabolic Systems with Multiple Time Delays Given in Integral Form

Bahaa G. M.1,2

1Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawwarah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

Received 1 March 2012; Accepted 29 April 2012

Academic Editor: Weihai Zhang

Copyright © 2012 Bahaa G. M.. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The optimal boundary control problem for ( 𝑛 × 𝑛 ) infinite order distributed parabolic systems with multiple time delays given in the integral form both in the state equations and in the Neumann boundary conditions is considered. Constraints on controls are imposed. Necessary and suffacient optimality conditions for the Neumann problem with the quadratic performance functional are derived.