TY - JOUR
AU - Al-hawasy, Jamil Amir
AU - Al-Qaisi, Safaa J. Mohammed
PY - 2019/08/15
Y2 - 2024/02/25
TI - The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints
JF - Al-Mustansiriyah Journal of Science
JA - Al-Mustansiriyah Journal of Science
VL - 30
IS - 1
SE - Mathematics
DO - 10.23851/mjs.v30i1.464
UR - https://mjs.uomustansiriyah.edu.iq/index.php/MJS/article/view/464
SP - 143-151
AB - This paper is concerned with, the proof of the existence and the uniqueness theorem for the solution of the state vector of a couple of nonlinear elliptic partial differential equations 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 adjoint equations associated with the considered couple of the state equations with equality and inequality constraints is studied. The necessary conditions theorem and the sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved using the Kuhn-Tucker-Lagrange multipliers theorems
ER -