@Article{,
title={The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations},
author={Jamil A. Ali Al-Hawasy and Ahmed Abdul Hasan Naeif},
journal={Al-Nahrain Journal of Science مجلة النهرين للعلوم},
volume={00},
number={1},
pages={123-136},
year={2018},
abstract={In this paper the continuous classical boundary optimal control problem of a couple nonlinear partial differential equations of parabolic type is studied. The Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution of a couple nonlinear parabolic partial differential equations for given (fixed) continuous classical boundary control vector. The theorem of the existence of a continuous classical optimal boundary control vector associated with the couple of nonlinear parabolic partial differential equations is proved. The existence of a unique vector solution of the adjoint equations is studied. The Fréchet derivative is derived; Finally The Kuhn-Tucker-Lagrange multipliers theorems is developed and then is used to prove the necessary conditions theorem and the sufficient conditions theorem of optimality of a couple of nonlinear parabolic equations with equality and inequality constraints.}
}