An Optimization Problem with Controls in the Coefficients of Parabolic Equations
M. H. Farag *
Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia and Mathematics Department, Faculty of Science, Minia University, Mina, Egypt.
T. A. Nofal
Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia and Mathematics Department, Faculty of Science, Minia University, Mina, Egypt.
Mohamed A. El-Sayed
CS Department, Faculty of Computer and Information Technology, Taif University, Taif, Saudi Arabia and Mathematics Department, Faculty of Science, Fayoum University, Fayoum, Egypt.
T. S. M. AL-Qarni
Faculty of Science and Arts, King Khalid University, Bbelkrn, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, an optimal control parabolic problem is studied. The existence and uniqueness theorem for the solving optimal control parabolic problem is proved. Also, a theorem for the sufficient differentiability conditions of the functional and its gradient formulae has been proved.
Keywords: Optimal control parabolic problems, existence and uniqueness theorems, adjoint system, sufficient differentiability conditions, gradient formulae.