The Continuous Classical Optimal Boundary Control of a Couple Linear Elliptic Partial Differential Equations

Abstract

This paper is concerned with the proof of the existence and uniqueness theorem for the solution of the state vector of a couple linear elliptic partial differential equations using the Galerkin method, where the continuous classical boundary control vector is given. Also, the existence theorem of a continuous classical boundary optimal control vector governed by the couple of linear elliptic partial differential equation is proved. The existence and the uniqueness solution of the couple of adjoint equations associated with the considered couple of the state equations studied. The derivation of the Fréchet derivative of the Hamiltonian is developed. The necessary conditions theorem of optimality of this problem is proved.