Classical Continuous Constraint Boundary Optimal Control Vector Problem for Triple Nonlinear Parabolic System

In this paper, our purpose is to study the classical continuous constraints boundary optimal triple control vector problem dominating nonlinear triple parabolic boundary value problem. The existence theorem for a classical continuous triple optimal control vector CCCBOTCV is stated and proved under suitable assumptions. The mathematical formulation of the adjoint triple boundary value problem associated with the nonlinear triple parabolic boundary value problem is discovered. The Fréchet derivative of the Hamiltonian is derived. Under proper assumptions, both theorems are granted; the necessary conditions for optimality and the sufficient conditions for optimality of the classical continuous constraints boundary optimal triple control vector problem are stated and proven.