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IMA Journal of Mathematical Control and Information 2002 19(4):461-476; doi:10.1093/imamci/19.4.461
© 2002 by Institute of Mathematics and its Applications
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Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay

W. Kotarski1, H. A. El-Saify2 and G. M. Bahaa2

1 Institute of Informatics, Silesian University, Bedzinska 60, 41-200 Sosnowiec, Poland 2 Mathematics Department, Faculty of Science, Branch of Cairo University, Beni Suef, Egypt

A distributed control problem for the parabolic operator with an infinite number of variables and time delay is considered. The performance index has an integral form. Constraints on controls are imposed. To obtain optimality conditions for the Neumann problem, the generalization of the Dubovitskii–Milyutin theorem given by Walczak in WALCZAK, S. Folia Mathematics, 1, 187–196 and WALCZAK, S. J. Optim. Theory Appl., 42, 561–582 was applied.

Keywords: optimal control problems; parabolic operators with an infinite number of variables with time delay; Dubovitskii–Milyutin theorem; conical approximations; optimality conditions; Weierstrass theorem.


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