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2D-1D dimensional reduction in a toy model for magnetoelastic interactions . (English) Zbl 1224.35058
Summary: The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

MSC:
35D30 Weak solutions to PDEs
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
35B40 Asymptotic behavior of solutions to PDEs
82D40 Statistical mechanics of magnetic materials
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References:
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