An Optimization Problem with Controls in the Coefficients of Parabolic Equations

M. H. Farag; T. A. Nofal; Mohamed A. El-Sayed; T. S. M. AL-Qarni

doi:10.9734/BJMCS/2015/14738

Research Article Open access CC BY 4.0

An Optimization Problem with Controls in the Coefficients of Parabolic Equations

M. H. Farag, T. A. Nofal, Mohamed A. El-Sayed, T. S. M. AL-Qarni

Journal of Advances in Mathematics and Computer Science · pp. 532–543 · Published 22 Jan 2015

10.9734/BJMCS/2015/14738

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.

Optimal control parabolic problems existence and uniqueness theorems adjoint system sufficient differentiability conditions gradient formulae.

Cited by 1

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

M. A. El-Sayed, M. Salama, M. Farag · 2017

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M. H. Farag, T. A. Nofal, Mohamed A. El-Sayed, T. S. M. AL-Qarni (2015). An Optimization Problem with Controls in the Coefficients of Parabolic Equations. Journal of Advances in Mathematics and Computer Science , 532–543. https://doi.org/10.9734/BJMCS/2015/14738

Affiliations

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.

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