Acta Mathematica Sinica

, Volume 22, Issue 2, pp 607–624

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


DOI: 10.1007/s10114-005-0688-0

Cite this article as:
Zhu, S.W. Acta Math Sinica (2006) 22: 607. doi:10.1007/s10114-005-0688-0


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.


Variational inequalitiesTime–delay operatorOptimal controlMaximum principle

MR (2000) Subject Classification


Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institute of MathematicsFudan UniversityShanghai 200433P. R. China
  2. 2.Department of Applied MatematicsShanxi Finance & Economics UniversityTaiyuan 030006P. R. China