Abstract
The Landau-Lifschitz equations describe the time-evolution of magnetization in classical ferro- and antiferromagnets and are of fundamental importance for the understanding of nonequilibrium magnetism. We sketch a proof that, under quite general conditions, dissipative forms of these equations have attracting sets which are finite-dimensional in a suitable sense. In particular, upper bounds are obtained for the Hausdorff and fractal dimensions of these sets.
On leave from the Department of Mathematics, Howard University, Washington, D.C. 20059.
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Gill, T.L., Zachary, W.W. (1987). Existence and finite-dimensionality of attractors for the Landau-Lifschitz equations. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080589
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DOI: https://doi.org/10.1007/BFb0080589
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