, Volume 22, Issue 2, pp 607-624
Date: 22 Feb 2006

Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives

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Abstract

In this paper, an optimal control problem for parabolic variational inequalities with delays in the highest order spatial derivatives is investigated. The well–posedness of such kinds of variational inequalities is established. The existence of optimal controls under a Cesari–type condition is proved, and the necessary conditions of Pontryagin type for optimal controls is derived.

This work is partially supported by the Chinese NSF under grant 101310310, the NSF under grant 10171059, the NSF under grant 10171030 the National Distinguished Youth Science Foundation of China under grant 10325101, and the Chinese Education Ministry Science Foundation under grant 20030246004