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Liu, H. and Yang, J. (2014) Optimal Control of Semi Linear Parabolic Systems with State Constraint. Journal of Mathematical Analysis and Applications, 417, 787-803.
https://doi.org/10.1016/j.jmaa.2014.03.070

has been cited by the following article:

• TITLE: The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems

  AUTHORS: Mohamed A. El-Sayed, Moustafa M. Salama, M. H. Farag, Fahad B. Al-Thobaiti

  KEYWORDS: Constrained Optimal Control Problems, Necessary Optimality Conditions Parabolic System, Adjoint Problem, Exterior Penalty Function Method, Existence and Uniqueness Theorems

  JOURNAL NAME: Open Journal of Optimization, Vol.6 No.1, March 23, 2017

  ABSTRACT: The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.