Guo, Boling; Han, Yongqian; Huang, Daiwen Weak and smooth global solution for Landau-Lifshitz-Bloch-Maxwell equation. (English) Zbl 1463.35383 Ann. Appl. Math. 36, No. 1, 1-30 (2020). Summary: This paper is devoted to investigate the existence and uniqueness of the solution of Landau-Lifshitz-Bloch-Maxwell equation. The Landau-Lifshitz-Bloch-Maxwell equation, which fits well for a wide range of temperature, is used to study the dynamics of magnetization vector in a ferromagnetic body. If the initial data is in \(({H^1}, {L^2}, {L^2})\), the existence of the global weak solution is established. If the initial data is in \(({H^{m+1}}, {H^m}, {H^m}) (m \ge 1)\), the existence and uniqueness of the global smooth solution are established. Cited in 1 Document MSC: 35N30 Overdetermined initial-boundary value problems for PDEs and systems of PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 35Q61 Maxwell equations Keywords:Landau-Lifshitz-Bloch-Maxwell equation; global solution; paramagnetic-ferromagnetic transition; temperature-dependent magnetic theory; Landau-Lifshitz theory PDFBibTeX XMLCite \textit{B. Guo} et al., Ann. Appl. Math. 36, No. 1, 1--30 (2020; Zbl 1463.35383)