Abstract
The paper begins with a fairly detailed presentation of a general mathematical model for the dynamics of ferromagnetic bodies undergoing arbitrarily large deformations. Next, a mathematical study is presented of the evolution problem for the magnetization field in a «soft» ferromagnetic body which is «mechanically at rest». No matter how special and simple this problem within the frame-work of the full theory, the governing equation is interesting: it is identical to the dynamic version of the harmonic-map equation usually referred to in the mathematical literature as the Gilbert form of the Landau-Lifshitz equation. Motivated by recent nonuniqueness results for the dynamic harmonicmap equation, we give a new proof of global existence of weak solutions to the Gilbert-Landau-Lifshitz equation.
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