Hamdache, Kamel; Hamroun, Djamila Existence of large solutions to the Landau-Lifshitz-Bloch equation. (English) Zbl 1462.35377 Commun. Math. Sci. 18, No. 2, 487-513 (2020). Summary: In this work we discuss existence of solutions of the Landau-Lifshitz-Bloch equation describing the dynamics of the magnetization for the whole range of the temperature. By using energy method we prove global existence of strong solutions for given initial data, existence of time-periodic solutions as well as existence of steady state solutions of the equation. Cited in 1 Document MSC: 35Q60 PDEs in connection with optics and electromagnetic theory 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35B10 Periodic solutions to PDEs 35D35 Strong solutions to PDEs 35B65 Smoothness and regularity of solutions to PDEs 35G31 Initial-boundary value problems for nonlinear higher-order PDEs 82D40 Statistical mechanics of magnetic materials 78A30 Electro- and magnetostatics Keywords:Landau-Lifshitz-Bloch equation; magnetization; anisotropic energy; magnetostatic equations; regularization method; Galerkin approximation; fixed-point theorems PDFBibTeX XMLCite \textit{K. Hamdache} and \textit{D. Hamroun}, Commun. Math. Sci. 18, No. 2, 487--513 (2020; Zbl 1462.35377) Full Text: DOI