Analysis and optimal control of some solidification processes
Roberto Carlos Cabrales, Gema Camacho, Enrique Fernández‐Cara · Discrete and Continuous Dynamical Systems · 2014
In this paper we consider a mathematical model that describes the solidification of a binary alloy. We prove some existence and uniqueness results for a regularized problem, depending on a small parameter $\epsilon$. We also analyze the behavior of the regularized solutions as $\epsilon \to 0$. Then, we consider some associated optimal control problems. We prove existence and optimality results and we present and discuss some iterative methods.