Quasi-stationary ferromagnetic problem for thin multi-structures. (English) Zbl 1454.78003
Summary: In this paper we study the asymptotic behavior of the solutions of time dependent micromagnetism problem in a multi-domain consisting of a thin-wire in junction with a thin film. We assume that the volumes of the two parts composing each multi-structure vanish with same rate. We obtain a \(1D\) limit problem on the thin-wire and a \(2D\) limit problem on the thin film, and the two limit problems are uncoupled. The limit problem remains non-convex, but now it becomes completely local.
MSC:
| 78A25 | Electromagnetic theory (general) |
| 74K35 | Thin films |
| 78M35 | Asymptotic analysis in optics and electromagnetic theory |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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