Optimal control of Landau-Lifshitz-Bloch equation with applied current

This paper deals with an optimal control problem of a mathematical model for current-induced magnetization dynamics in ferromagnets at elevated temperatures described by the classical Landau-Lifshitz-Bloch (LLB) equation involving adiabatic torque where the control is given by the applied current. We prove the existence of an optimal control and then we derive the first-order necessary optimality system for the optimal solution by using the Lagrange multiplier method. Some regularity properties of the adjoint and the optimal control are also discussed.