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On controllability of a two-dimensional network of ferromagnetic ellipsoidal samples. (English) Zbl 1414.93035

Summary: 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 nonlinear 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.

MSC:

93B05 Controllability
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
82D40 Statistical mechanics of magnetic materials
35Q60 PDEs in connection with optics and electromagnetic theory
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