Optimality Conditions for Semilinear Hyperbolic Systems with Distributed Control

Abstract

In this paper we investigate an optimal control problem for semilinear hyperbolic systems with unknown initial data. We first give some general existence results and then derive optimality conditions via a penalization method. Finally, we apply our abstract results to an example.

Keywords:

• Optimal control penalization
• Semilinear hyperbolic system
• Optimality conditions
• 2000 Mathematics Subject Classification: 93-xx
• 49J20
• 49K20

Acknowledgment

This work was supported by Grant No. R01-2002-000-00491-0 from the Korea Science and Engineering Foundation.