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

Authors

  • Jamil A Ali Al-Hawasy Department of Math., College of Science, Al-Mustansiriyah University, Baghdad-Iraq.
  • Ahmed Abdul Hasan Naeif Department of Math., College of Science, Al-Mustansiriyah University, Baghdad-Iraq.

Keywords:

boundary optimal control, couple nonlinear parabolic partial differential equations

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.

Published

2018-10-25

Issue

Section

Articles

How to Cite

(1)
The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Parabolic Partial Differential Equations. ANJS 2018, No. 1, 123-136.