Zhong, Penghong; Wang, Shu; Guo, Boling Some blowup solutions about two systems derived from Landau-Lifshitz-Gilbert equation. (English) Zbl 1281.78008 Appl. Math. Modelling 37, No. 6, 4177-4188 (2013). 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. Reviewer: Aleksander Pankov (Baltimore) Cited in 1 Document MSC: 78A25 Electromagnetic theory (general) 35B44 Blow-up in context of PDEs Keywords:Landau-Lifshitz-Gilbert equation; harmonic map; heat flow; blow up PDFBibTeX XMLCite \textit{P. Zhong} et al., Appl. Math. Modelling 37, No. 6, 4177--4188 (2013; Zbl 1281.78008) Full Text: DOI Link