Robust and Optimal Control Problems to a Phase-Field Model for the Solidification of a Binary Alloy with a Constant Temperature

Abstract

In this paper, we consider robust control problems which are governed by a two-dimensional phase-field model of Warren—Boettinger, which describes the solidification of a binary alloy, in order to take into account the influence of noises in the data. Firstly, the robust control problems are formulated. Afterwards, the existence and uniqueness of the solution of the perturbation (of the nonlinear governing system of equations) is proved as well as stability under mild assumptions. We prove the existence of an optimal solution, and we also find necessary optimality conditions.