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Control of the Landau-Lifshitz equation. (English) Zbl 1335.93108

Summary: The Landau-Lifshitz equation describes the dynamics of magnetization inside a ferromagnet. This equation is nonlinear and has an infinite number of stable equilibria. It is desirable to control the system from one equilibrium to another. A control that moves the system from an arbitrary initial state, including an equilibrium point, to a specified equilibrium is presented. It is proven that the second point is an asymptotically stable equilibrium of the controlled system. The results are illustrated with some simulations.

MSC:

93D20 Asymptotic stability in control theory
35Q60 PDEs in connection with optics and electromagnetic theory
93C20 Control/observation systems governed by partial differential equations
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