The Optimal Control For The Free Boundary Of One-phase Stefan Problem

We investigate in this article the optimal control problem for the one-phase Stefan problem: with the control function forced on the fixed endpoint (i.e. the left endpoint) and the free boundary (i.e. the right endpoint) being moved by s(t). The purpose for the control is expected to let the free boundary track the given location. At first, the existence and u-niqueness of the solution for the Stefan problem have been solved,namely, the existence and uniqueness for temperature and free boundary have been solved. Then we should consider two aspecs below in this article:one is the existence of the optimal control, employing the weak*convergence of the minimizing sequence and Mazur theorem; The other is to give the necesarry condition for the existence of the optimal control by the linearization method for the established indicators of functional.