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Some blowup solutions about two systems derived from Landau-Lifshitz-Gilbert equation. (English) Zbl 1281.78008

Authors’ abstract: Two different systems which can be regarded as the extreme cases the of Landau-Lifshitz-Gilbert equation are considered. When the gyromagnetic term of the Landau-Lifshitz-Gilbert equation vanishes, we consider some special solutions for a modified harmonic map heat flow which map from \((2+1)\)-dimensional space-time into the \(2\)-sphere. The existence of regular initial data leading to blow up in finite time is established. When the Gilbert term is omitted, a blowup solution is obtained by constructing a blowup solution of the Landau-Lifshitz equation.

MSC:

78A25 Electromagnetic theory (general)
35B44 Blow-up in context of PDEs
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