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The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations

Ahmed Abdul Hasan Naeif --- Jamil A. Ali Al-Hawasy

Al-Nahrain Journal of Science مجلة النهرين للعلوم
ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 00 Issue: 1 Pages: 123-136
Publisher: Al-Nahrain University جامعة النهرين

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.

Keywords

boundary optimal control --- couple nonlinear parabolic partial differential equations.