Constraints Optimal Classical Continuous Control Vector Problem for Quaternary Nonlinear Hyperbolic System

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints optimal classical continuous control vector (CQOCCCV), cost function (CF), and equality inequality state (EIQSCCV). The existence of a CQOCCCV dominating by QNLHBVP stated demonstrated using Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, mathematical formulation adjoint equations (QAEs) related to (QSE) are discovere so as its weak form (WF) . directional derivative (DD) Hamiltonian (Ham) calculated. necessary sufficient conditions for optimality (NCSO) theorems proposed proved.