Zhu, Shang Wei, Optimal Control of Variational Inequalities with Delays in the Highest Order Spatial Derivatives, Acta mathematica Sinica. English series (Print) , 22(2), 2006, pp. 607-624
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.