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Archive for Rational Mechanics and Analysis

, Volume 233, Issue 3, pp 1383–1440 | Cite as

On Stochastic Optimal Control in Ferromagnetism

  • Thomas Dunst
  • Ananta K. Majee
  • Andreas ProhlEmail author
  • Guy Vallet
Article
  • 38 Downloads

Abstract

A model is proposed to, e.g., control the domain wall motion in ferromagnets in the presence of thermal fluctuations, and the existence of an optimal stochastic control process is proved. The convergence of a finite element approximation of the problem is shown in space-dimension one, which then allows one to apply Pontryagin’s maximum principle for this finite dimensional setting. The resulting coupled system of forward-backward stochastic differential equations is numerically solved by means of the stochastic gradient method to enable practical simulations.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany
  2. 2.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia
  3. 3.Laboratoire de Mathématiques et de leurs Applications de Pau IPRA, UMR5142IFCAM UMI CNRS 3494, CNRS/Univ Pau & Pays AdourPauFrance

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