The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints

  • Jamil A. Ali Al-Hawasy Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
  • Nabeel A. Thyab Al-Ajeeli Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Keywords: optimal control vector, triple nonlinear elliptic equations, necessary and sufficient conditions for optimality

Abstract

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations related with the triple state equations.

The Fréchet derivative is obtained. Finally we prove the theorems of both the necessary and sufficient conditions for optimality of the triple nonlinear partial differential equations of elliptic type through the Kuhn-Tucker-Lagrange's Multipliers theorem with equality and inequality constraints.

Published
2021-09-30
How to Cite
Al-Hawasy, J. A. A., & Al-Ajeeli, N. A. T. (2021). The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints. Iraqi Journal of Science, 62(9), 3020-3030. https://doi.org/10.24996/ijs.2021.62.9.17
Section
Mathematics