@inbook{d61f20e2abbf4507b0ed92c9731d275e,
title = "The Dubovitskii and Milyutin formalism applied to an optimal control problem in a solidification model",
abstract = "In this paper we study an optimal control problem in a physical system governed by a solidification model. The solidification system is given by a nonlinear parabolic PDE system of two equations for the unknowns the (reduced) temperature and a phase field function, with a temperature source term. The optimal control problem is defined via the source term as the control function and the objective functional given by the comparison in L2n-norms of the real state with a given target state and the cost of the control. The main results of the paper are the existence of a global optimal solution via a minimizing sequence, and the first-order necessary conditions for local optimal solutions, by means of the application of the Dubovitskii and Milyutin formalism.",
keywords = "Diffuse-interface phase field, Optimal control, Optimality conditions, Parabolic systems, Solidification",
author = "An{\'i}bal Coronel and Francisco Guill{\'e}n-Gonz{\'a}lez and Francisco Marques-Lopes and Marko Rojas-Medar",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2018.",
year = "2018",
doi = "10.1007/978-3-319-97613-6\_11",
language = "English",
series = "SEMA SIMAI Springer Series",
publisher = "Springer Nature",
pages = "211--231",
booktitle = "SEMA SIMAI Springer Series",
address = "Germany",
}