Optimal control in stochastic Landau-Lifshitz-Gilbert equation

Abstract: 

In this presentation, we study an optimal control problem for the stochastic Landau-Lifshitz-Gilbert equation on a bounded domain in R^d (d = 1, 2, 3). We first establish existence of a relaxed optimal control for the relaxed version of the problem. As the control acts linearly in the equation, we then establish existence of an optimal control for the underlying problem. Furthermore, convergence of a structure preserving finite element approximation for d = 1 and physically relevant computational studies will be discussed.