### The Solvability of the Continuous Classical Boundary Optimal Control of Couple Nonlinear Elliptic Partial Differential Equations with State Constraints

*Al-Mustansiriyah Journal of Science*

2019, Volume 30, Issue 1, Pages 143-151

2019, Volume 30, Issue 1, Pages 143-151

#### Abstract

This paper concerns with, the proof of the existence and the uniqueness theorem for the solution of the state vector of couple of nonlinear elliptic partial differential equations by using the Minty-Browder theorem, where the continuous classical boundary control vector is given. Also the existence theorem of a continuous classical boundary optimal control vector governing by the couple of nonlinear elliptic partial differential equation with equality and inequality constraints is proved. The existence of the uniqueness solution of the couple of adjoin equations which is associated with the couple of the state equations with equality and inequality constraints is studied. The necessary and sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved by using the Kuhn-Tucker-Lagrange multipliers theorems.

#### Keywords

Classical boundary optimal control, couple of nonlinear elliptic partial differential equations, necessary and sufficient conditions.#### Metrics