The necessary condition for optimal boundary control problems for triple elliptic partial differential equations

الملخص EN

In this work, we prove that the triple linear partial differential equations (PDEs) of theelliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr)has a unique "state" solution vector (SSV) by utilizing the Galerkin's method (GME).

Also, weprove the existence of a classical continuous boundary optimal control vector (CCBOCVr)ruled by the TLEPDEs.

We study the existence solution for the triple adjoint equations (TAJEs)related with the triple state equations (TSEs).

The Fréchet derivative (FDe) for the objectivefunction is derived.

At the end we prove the necessary "conditions" theorem (NCTh) foroptimality for the In this work, we prove that the triple linear partial differential equations (PDEs) of theelliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr)has a unique "state" solution vector (SSV) by utilizing the Galerkin's method (GME).

Also, weprove the existence of a classical continuous boundary optimal control vector (CCBOCVr)ruled by the TLEPDEs.

We study the existence solution for the triple adjoint equations (TAJEs)related with the triple state equations (TSEs).

The Fréchet derivative (FDe) for the objectivefunction is derived.

At the end we prove the necessary "conditions" theorem (NCTh) foroptimality for the problem.