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Русская версия

**G. M. Bahaa**

Mathematics Department,

Faculty of Science,

Beni-Suef University, Beni- Suef, Egypt

A time optimal control problem for infnite order parabolic equations is considered. A time optimal control problem is replaced by an equivalent one with a performance index in the form of integral form. Constraints on controls are assumed. To obtain the optimality conditions for the Neumann problem, the generalization of the Dubovitskii-Milyutin Theorem given by Walczak in Refs.[41,42] was applied.