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Optimal Stochastic Control in Ferromagnetism

The stochastic Landau-Lifshitz Gilbert equation is a SPDE describing ferromagnetism in the presence of thermal fluctuations. The main focus in my talk is an optimal control problem to e.g. control domain wall motion in ferromagnetic devices at elevated temperatures.

I discuss main steps to construct a solution to this problem. In one space dimension, I discuss convergence of a finite element discretization, for which Pontryagin’s maximum principle may then be applied. The resulting coupled system of forward-backward SDEs is numerically solved by means of the stochastic gradient method, and simulations will be reported. - This is joint work with A. Majee, T. Dunst (both U Tuebingen), and G. Vallet (U Pau).

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