International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1703-1714
doi:10.1155/S0161171203209273

Duality in the optimal control for damped hyperbolic systems with positive control

Mi Jin Lee,1 Jong Yeoul Park,1 and Young Chel Kwon2

1Department of Mathematics, Pusan National University (PNU), Pusan 609–735, Korea
2Department of Mathematics, Dong-A University, Pusan 604–714, Korea

Received 10 September 2002

Copyright © 2003 Mi Jin Lee et al. 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

We study the duality theory for damped hyperbolic equations. These systems have positive controls and convex cost functionals. Our main results lie in the application of duality theorem, that is, inf J=sup K, on various cost functions.