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On Controllability of a Two-Dimensional Network of Ferromagnetic Ellipsoidal Samples

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Abstract

In this article, we address the problem of stability and controllability of two-dimensional network of ferromagnetic particles of ellipsoidal shapes. The dynamics of magnetization inside the ferromagnetic material is governed by the Landau–Lifschitz equation of micromagnetism which is non-linear and parabolic in nature. The control is the magnetic field generated by a dipole whose position and amplitude can be selected. In the absence of control, first we prove the exponential stability of the relevant configurations of the network. Then, we investigate the controllability by the means of external magnetic field induced by the magnetic dipole.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Shruti Dubey

  2. SRM Research Institute and Department of Mathematics, SRM Institute of Science and Technology, Chennai, 603 203, India

    Sharad Dwivedi

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  1. Shruti Dubey
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  2. Sharad Dwivedi
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Correspondence to Shruti Dubey.

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Dubey, S., Dwivedi, S. On Controllability of a Two-Dimensional Network of Ferromagnetic Ellipsoidal Samples. Differ Equ Dyn Syst 27, 277–297 (2019). https://doi.org/10.1007/s12591-018-0407-9

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  • DOI: https://doi.org/10.1007/s12591-018-0407-9

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